# American Institute of Mathematical Sciences

• Previous Article
Analysis of a dynamic premium strategy: From theoretical and marketing perspectives
• JIMO Home
• This Issue
• Next Article
Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process
October  2018, 14(4): 1521-1544. doi: 10.3934/jimo.2018019

## Optimal pricing and inventory management for a loss averse firm when facing strategic customers

 1 Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China 2 Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China

* Corresponding author: Jinting Wang

Received  February 2017 Revised  July 2017 Published  January 2018

Fund Project: This work is supported in part by the National Natural Science Foundation of China (Grant nos. 71571014,71390334.).

This paper considers the joint inventory and pricing decision problem that a loss averse firm with reference point selling seasonal products to strategic consumers with risk preference and decreasing value. Consumers can decide whether to buy at the full price in stage 1, or to wait till stage 2 for the salvage price. They may not get the product if the product is sold out in stage 2. The firm aims to choose a base stock policy and find an optimal price to maximize its expected utility, while consumers aim to decide whether to buy or wait strategically for optimizing their payoffs. We formulate the problem as a Stackelberg game between the firm and the strategic consumers in which the firm is the leader. By deriving the rational expectation equilibrium, we find both the optimal stocking level and the full price in our model are lower than those in the classical model without strategic consumers, by which leads to a lower profit. Furthermore, it is shown that the reimbursement contract cannot alleviate the impact of strategic behavior of customers while the firm's profit can be improved by the price commitment strategy in most cases. Numerical studies are carried out to investigate the impact of strategic customer behavior and system parameters on the firm's optimal decisions.

Citation: Ruopeng Wang, Jinting Wang, Chang Sun. Optimal pricing and inventory management for a loss averse firm when facing strategic customers. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1521-1544. doi: 10.3934/jimo.2018019
##### References:

show all references

##### References:
Two-stage decision model
Impact of customer's risk preference on the firm's decisions in different $\alpha$ and $\delta$
Effect of decreasing rate on the firm's decision variables in different values $\alpha$ and $\lambda$
The firm's expected profit changes with $\alpha$ and $\lambda$
The pattern of the firm's expected profit.
The pattern of the firm's expected profit
Classification of literature on pricing and inventory control with strategic customers
 Contributions Risk preference of Customers Decreasing value Loss aversion Su & Zhang (2008) - - - Liu & Van (2008) $\surd$ - - Aviv & Pazgal (2008) - $\surd$ - Du, Zhang & Hua (2015) $\surd$ $\surd$ - This paper $\color{red}\surd$ $\color{red}\surd$ $\color{red}\surd$
 Contributions Risk preference of Customers Decreasing value Loss aversion Su & Zhang (2008) - - - Liu & Van (2008) $\surd$ - - Aviv & Pazgal (2008) - $\surd$ - Du, Zhang & Hua (2015) $\surd$ $\surd$ - This paper $\color{red}\surd$ $\color{red}\surd$ $\color{red}\surd$
Parameters and notations
 Notation Description $p_{0}^{*}$, $p_{\alpha}^{*}$ and $p_{r}^{*}$ The full price of unit product in classical model, the model with strategic customers and the model with reimbursement contract, respectively in period 1 $Q_{0}^{*}$, $Q_{\alpha}^{*}$ and $Q_{r}^{*}$ The stocking quantity in classical model, the model with strategic customers and the model with reimbursement contract, respectively $Q$, $p$ Decision variables denoting stocking quantity and full price, respectively $D$ Nonnegative and independent random variable, which indicates customers' demand $F(x)$ Cumulative distribution function, characterizing the demand, and tail distribution is $\overline{F}(x)]=1-F(x)$ $G(x)$ Partial expectation of random $D$, which is defined as $G(x)=\int_{0}^{x}Df(D)dD$ $s$ Salvage price in period 2 $c$ Unit procurement cost of the product to the firm $V$ Customers' valuation for the unit production $r$ Customers' reservation price or maximum price which the customers are willing to pay $\xi_{r}$ The firm's belief over customers' reservation price $\xi_{prob}$ Customers' belief from obtaining the product on the salvage market $\delta$ The decreasing rate ($0<\delta\leq1$) $\lambda$ Customers' risk preference ($\lambda>0$) $\alpha$ The firm's loss aversion ($\alpha\geq1$) $E(\cdot)$ Expectation operator $U(\cdot)$ Utility function of the firm $x^{+}$ and $x^{-}$ The maximum and minimal function between $0$ and $x$, respectively. $x^{+}=\max\{0, x\}$ and $x^{-}=\min\{0, x\}$
 Notation Description $p_{0}^{*}$, $p_{\alpha}^{*}$ and $p_{r}^{*}$ The full price of unit product in classical model, the model with strategic customers and the model with reimbursement contract, respectively in period 1 $Q_{0}^{*}$, $Q_{\alpha}^{*}$ and $Q_{r}^{*}$ The stocking quantity in classical model, the model with strategic customers and the model with reimbursement contract, respectively $Q$, $p$ Decision variables denoting stocking quantity and full price, respectively $D$ Nonnegative and independent random variable, which indicates customers' demand $F(x)$ Cumulative distribution function, characterizing the demand, and tail distribution is $\overline{F}(x)]=1-F(x)$ $G(x)$ Partial expectation of random $D$, which is defined as $G(x)=\int_{0}^{x}Df(D)dD$ $s$ Salvage price in period 2 $c$ Unit procurement cost of the product to the firm $V$ Customers' valuation for the unit production $r$ Customers' reservation price or maximum price which the customers are willing to pay $\xi_{r}$ The firm's belief over customers' reservation price $\xi_{prob}$ Customers' belief from obtaining the product on the salvage market $\delta$ The decreasing rate ($0<\delta\leq1$) $\lambda$ Customers' risk preference ($\lambda>0$) $\alpha$ The firm's loss aversion ($\alpha\geq1$) $E(\cdot)$ Expectation operator $U(\cdot)$ Utility function of the firm $x^{+}$ and $x^{-}$ The maximum and minimal function between $0$ and $x$, respectively. $x^{+}=\max\{0, x\}$ and $x^{-}=\min\{0, x\}$
Numerical results for various systems of expected profit when $s = 2$ and $V = 15$
 $\alpha=1$ $\alpha=2$ $\alpha=3$ $\delta=0.25$ $\delta=0.5$ $\delta=1$ $\delta=0.25$ $\delta=0.5$ $\delta=1$ $\delta=0.25$ $\delta=0.5$ $\delta=1$ 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red} {\pmb {406.6204}}$ 298.9421 162.4174 $\color{red}{\pmb {408.1164}}$ 304.5730 175.2384 $\color{red}{\pmb {409.3841}}$ 309.4728 185.7115 $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {403.3333}}$ 403.3333 403.3333 $\color{green}{\pmb {402.8578}}$ 402.8578 402.8578 $\color{green}{\pmb {401.5556}}$ 401.5556 401.5556 $\Pi_{p}^{*}$ 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 $\Pi_{0}^{*}$ $c=4$ $\lambda=1$ 394.9592 260.6531 94.1742 395.8801 264.8910 105.3170 396.6050 268.5129 113.9793 $\Pi_{\alpha}^{*}$ 403.3333 403.3333 403.3333 402.8578 402.8578 402.8578 401.5556 401.5556 401.5556 $\Pi_{p}^{*}$ 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 $\Pi_{0}^{*}$ $\lambda=2$ 388.0647 235.1442 46.7179 388.5513 237.8978 54.9701 388.8571 240.1336 60.9781 $\Pi_{\alpha}^{*}$ 403.3333 403.3333 403.3333 402.8578 402.8578 402.8578 401.5556 401.5556 401.5556 $\Pi_{p}^{*}$ 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red}{\pmb {338.1945}}$ 256.3412 154.3494 $\color{red}{\pmb {340.4831}}$ 264.0884 169.3020 $\color{red}{\pmb {341.9950}}$ 270.0823 180.6548 $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {333.3333}}$ 333.3333 333.3333 $\color{green}{\pmb {332.4099}}$ 332.4099 332.4099 $\color{green}{\pmb {330}}$ 330 330 $\Pi_{p}^{*}$ 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 $\Pi_{0}^{*}$ $c=5$ $\lambda=1$ 323.4039 212.4169 84.3076 324.9323 218.7253 96.7836 325.7676 223.4203 105.7881 $\Pi_{\alpha}^{*}$ 333.3333 333.3333 333.3333 332.4099 332.4099 332.4099 330 330 330 $\Pi_{p}^{*}$ 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 $\Pi_{0}^{*}$ $\lambda=2$ 313.9245 180.8531 36.9033 314.7191 185.1787 45.1564 314.8643 188.0670 50.7402 $\Pi_{\alpha}^{*}$ 333.3333 333.3333 333.3333 332.4099 332.4099 332.4099 330 330 330 $\Pi_{p}^{*}$ 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red}{\pmb {275.9692}}$ 214.7582 138.5999 $\color{red}{\pmb {278.5443}}$ 223.2811 153.8583 $\color{red}{\pmb {279.5104}}$ 228.8967 164.4633 $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {270}}$ 270 270 $\color{green}{\pmb {268.5185}}$ 268.5185 268.5185 $\color{green}{\pmb {264.8633}}$ 264.8633 264.8633 $\Pi_{p}^{*}$ 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 $\Pi_{0}^{*}$ $c=6$ $\lambda=1$ 259.6189 169.7678 71.4952 261.4923 177.1413 83.8399 261.8907 181.7852 92.0999 $\Pi_{\alpha}^{*}$ 270 270 270 268.5185 268.5185 268.5185 264.8633 264.8633 264.8633 $\Pi_{p}^{*}$ 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 $\Pi_{0}^{*}$ $\lambda=2$ 248.2615 135.5270 27.4710 249.1956 140.7354 34.7699 248.7501 143.5081 39.4236 $\Pi_{\alpha}^{*}$ 270 270 270 268.5185 268.5185 268.5185 264.8633 264.8633 264.8633 $\Pi_{p}^{*}$ 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red}{\pmb {32.8174}}$ 29.5585 24.7304 $\color{red}{\pmb {31.7544}}$ $\color{red}{\pmb {29.7348}}$ 26.4622 $\color{red}{\pmb {29.1689}}$ $\color{red}{\pmb {27.8619}}$ $\color{red}{\pmb {25.6263}}$ $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {30}}$ 30 30 $\color{green}{\pmb {28.2369}}$ $\color{green}{\pmb {28.2369}}$ 28.2369 $\color{green}{\pmb {25.4313}}$ $\color{green}{\pmb {25.4313}}$ $\color{green}{\pmb {25.4313}}$ $\Pi_{p}^{*}$ 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 $\Pi_{0}^{*}$ $c=12$ $\lambda=1$ 27.4769 17.5997 8.61672 27.3621 19.2783 10.8693 $\color{red}{\pmb {25.6164}}$ 19.0687 11.674 $\Pi_{\alpha}^{*}$ 30 30 30 28.2369 28.2369 28.2369 $\color{green}{\pmb {25.4313}}$ 25.4313 25.4313 $\Pi_{p}^{*}$ 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 $\Pi_{0}^{*}$ $\lambda=2$ 20.6633 6.42676 0.8171 20.8133 7.6716 1.2734 19.6287 7.9764 1.5628 $\Pi_{\alpha}^{*}$ 30 30 30 28.2369 28.2369 28.2369 25.4313 25.4313 25.4313 $\Pi_{p}^{*}$ Note: The expected profits are the classical inventory model, the proposed model and the model under price commitment strategy in turn. We mark by red and green color when the expected profit of our model is larger than that of under price commitment strategy model.
 $\alpha=1$ $\alpha=2$ $\alpha=3$ $\delta=0.25$ $\delta=0.5$ $\delta=1$ $\delta=0.25$ $\delta=0.5$ $\delta=1$ $\delta=0.25$ $\delta=0.5$ $\delta=1$ 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red} {\pmb {406.6204}}$ 298.9421 162.4174 $\color{red}{\pmb {408.1164}}$ 304.5730 175.2384 $\color{red}{\pmb {409.3841}}$ 309.4728 185.7115 $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {403.3333}}$ 403.3333 403.3333 $\color{green}{\pmb {402.8578}}$ 402.8578 402.8578 $\color{green}{\pmb {401.5556}}$ 401.5556 401.5556 $\Pi_{p}^{*}$ 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 $\Pi_{0}^{*}$ $c=4$ $\lambda=1$ 394.9592 260.6531 94.1742 395.8801 264.8910 105.3170 396.6050 268.5129 113.9793 $\Pi_{\alpha}^{*}$ 403.3333 403.3333 403.3333 402.8578 402.8578 402.8578 401.5556 401.5556 401.5556 $\Pi_{p}^{*}$ 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 465.3846 $\Pi_{0}^{*}$ $\lambda=2$ 388.0647 235.1442 46.7179 388.5513 237.8978 54.9701 388.8571 240.1336 60.9781 $\Pi_{\alpha}^{*}$ 403.3333 403.3333 403.3333 402.8578 402.8578 402.8578 401.5556 401.5556 401.5556 $\Pi_{p}^{*}$ 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red}{\pmb {338.1945}}$ 256.3412 154.3494 $\color{red}{\pmb {340.4831}}$ 264.0884 169.3020 $\color{red}{\pmb {341.9950}}$ 270.0823 180.6548 $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {333.3333}}$ 333.3333 333.3333 $\color{green}{\pmb {332.4099}}$ 332.4099 332.4099 $\color{green}{\pmb {330}}$ 330 330 $\Pi_{p}^{*}$ 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 $\Pi_{0}^{*}$ $c=5$ $\lambda=1$ 323.4039 212.4169 84.3076 324.9323 218.7253 96.7836 325.7676 223.4203 105.7881 $\Pi_{\alpha}^{*}$ 333.3333 333.3333 333.3333 332.4099 332.4099 332.4099 330 330 330 $\Pi_{p}^{*}$ 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 384.6154 $\Pi_{0}^{*}$ $\lambda=2$ 313.9245 180.8531 36.9033 314.7191 185.1787 45.1564 314.8643 188.0670 50.7402 $\Pi_{\alpha}^{*}$ 333.3333 333.3333 333.3333 332.4099 332.4099 332.4099 330 330 330 $\Pi_{p}^{*}$ 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red}{\pmb {275.9692}}$ 214.7582 138.5999 $\color{red}{\pmb {278.5443}}$ 223.2811 153.8583 $\color{red}{\pmb {279.5104}}$ 228.8967 164.4633 $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {270}}$ 270 270 $\color{green}{\pmb {268.5185}}$ 268.5185 268.5185 $\color{green}{\pmb {264.8633}}$ 264.8633 264.8633 $\Pi_{p}^{*}$ 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 $\Pi_{0}^{*}$ $c=6$ $\lambda=1$ 259.6189 169.7678 71.4952 261.4923 177.1413 83.8399 261.8907 181.7852 92.0999 $\Pi_{\alpha}^{*}$ 270 270 270 268.5185 268.5185 268.5185 264.8633 264.8633 264.8633 $\Pi_{p}^{*}$ 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 311.5384 $\Pi_{0}^{*}$ $\lambda=2$ 248.2615 135.5270 27.4710 249.1956 140.7354 34.7699 248.7501 143.5081 39.4236 $\Pi_{\alpha}^{*}$ 270 270 270 268.5185 268.5185 268.5185 264.8633 264.8633 264.8633 $\Pi_{p}^{*}$ 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 $\Pi_{0}^{*}$ $\lambda=0.5$ $\color{red}{\pmb {32.8174}}$ 29.5585 24.7304 $\color{red}{\pmb {31.7544}}$ $\color{red}{\pmb {29.7348}}$ 26.4622 $\color{red}{\pmb {29.1689}}$ $\color{red}{\pmb {27.8619}}$ $\color{red}{\pmb {25.6263}}$ $\Pi_{\alpha}^{*}$ $\color{green}{\pmb {30}}$ 30 30 $\color{green}{\pmb {28.2369}}$ $\color{green}{\pmb {28.2369}}$ 28.2369 $\color{green}{\pmb {25.4313}}$ $\color{green}{\pmb {25.4313}}$ $\color{green}{\pmb {25.4313}}$ $\Pi_{p}^{*}$ 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 $\Pi_{0}^{*}$ $c=12$ $\lambda=1$ 27.4769 17.5997 8.61672 27.3621 19.2783 10.8693 $\color{red}{\pmb {25.6164}}$ 19.0687 11.674 $\Pi_{\alpha}^{*}$ 30 30 30 28.2369 28.2369 28.2369 $\color{green}{\pmb {25.4313}}$ 25.4313 25.4313 $\Pi_{p}^{*}$ 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 96.1538 $\Pi_{0}^{*}$ $\lambda=2$ 20.6633 6.42676 0.8171 20.8133 7.6716 1.2734 19.6287 7.9764 1.5628 $\Pi_{\alpha}^{*}$ 30 30 30 28.2369 28.2369 28.2369 25.4313 25.4313 25.4313 $\Pi_{p}^{*}$ Note: The expected profits are the classical inventory model, the proposed model and the model under price commitment strategy in turn. We mark by red and green color when the expected profit of our model is larger than that of under price commitment strategy model.
 [1] Manuel Friedrich, Martin Kružík, Ulisse Stefanelli. Equilibrium of immersed hyperelastic solids. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021003 [2] Ripeng Huang, Shaojian Qu, Xiaoguang Yang, Zhimin Liu. Multi-stage distributionally robust optimization with risk aversion. Journal of Industrial & Management Optimization, 2021, 17 (1) : 233-259. doi: 10.3934/jimo.2019109 [3] Juhua Shi, Feida Jiang. The degenerate Monge-Ampère equations with the Neumann condition. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020297 [4] Wenyan Zhuo, Honglin Yang, Leopoldo Eduardo Cárdenas-Barrón, Hong Wan. Loss-averse supply chain decisions with a capital constrained retailer. Journal of Industrial & Management Optimization, 2021, 17 (2) : 711-732. doi: 10.3934/jimo.2019131 [5] Nan Zhang, Linyi Qian, Zhuo Jin, Wei Wang. Optimal stop-loss reinsurance with joint utility constraints. Journal of Industrial & Management Optimization, 2021, 17 (2) : 841-868. doi: 10.3934/jimo.2020001 [6] Ugo Bessi. Another point of view on Kusuoka's measure. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020404 [7] Mengni Li. Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions. Communications on Pure & Applied Analysis, 2021, 20 (1) : 301-317. doi: 10.3934/cpaa.2020267 [8] Ömer Arslan, Selçuk Kürşat İşleyen. A model and two heuristic methods for The Multi-Product Inventory-Location-Routing Problem with heterogeneous fleet. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021002 [9] Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021013 [10] Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020451 [11] Kung-Ching Chang, Xuefeng Wang, Xie Wu. On the spectral theory of positive operators and PDE applications. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3171-3200. doi: 10.3934/dcds.2020054 [12] Jia Cai, Guanglong Xu, Zhensheng Hu. Sketch-based image retrieval via CAT loss with elastic net regularization. Mathematical Foundations of Computing, 2020, 3 (4) : 219-227. doi: 10.3934/mfc.2020013 [13] Evelyn Sander, Thomas Wanner. Equilibrium validation in models for pattern formation based on Sobolev embeddings. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 603-632. doi: 10.3934/dcdsb.2020260 [14] Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020320 [15] Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial & Management Optimization, 2021, 17 (1) : 357-368. doi: 10.3934/jimo.2019115 [16] Sabira El Khalfaoui, Gábor P. Nagy. On the dimension of the subfield subcodes of 1-point Hermitian codes. Advances in Mathematics of Communications, 2021, 15 (2) : 219-226. doi: 10.3934/amc.2020054 [17] Balázs Kósa, Karol Mikula, Markjoe Olunna Uba, Antonia Weberling, Neophytos Christodoulou, Magdalena Zernicka-Goetz. 3D image segmentation supported by a point cloud. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 971-985. doi: 10.3934/dcdss.2020351 [18] Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020458 [19] Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 [20] Tuoc Phan, Grozdena Todorova, Borislav Yordanov. Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1071-1099. doi: 10.3934/dcds.2020310

2019 Impact Factor: 1.366