
ISSN:
1534-0392
eISSN:
1553-5258
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Communications on Pure & Applied Analysis
September 2018 , Volume 17 , Issue 5
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By using critical point theory, we obtain some new sufficient conditions on the existence of homoclinic solutions of a class of nonlinear discrete
This paper is concerned with the elliptic system
where
In this work we study the following quasilinear elliptic equation:
where
We derive a new Liouville type result for a kind of "broken equation". This result together with blow-up techniques, a priori estimates and a fixed-point result of Krasnosel'skii, allow us to ensure the existence of a positive radial solution. In this paper we also obtain a non-existence result, proven through a variation of the Pohozaev identity.
This paper is devoted to the analysis of blow-up solutions for the fractional nonlinear Schrödinger equation with combined power-type nonlinearities
where
In this paper, we revisit the singular Non-Newton polytropic filtration equation, which was studied extensively in the recent years. However, all the studies are mostly concerned with subcritical initial energy, i.e.,
We study free boundary problem of Fisher-KPP equation
In this paper we will give a trichotomy result, that is, for any initial data, exactly one of the three behaviors, vanishing, spreading and transition, happens. This result is related to the results appear in the free boundary problem for the Fisher-KPP equation with a shifting-environment, which was considered by Du, Wei and Zhou [
In this paper, we establish a global Carleman estimate for the Kawahara equation. Based on this estimate, we obtain the Unique Continuation Property (UCP) for this equation and the global exponential stability for the Kawahara equation with a very weak localized dissipation.
We study a Kirchhoff type elliptic equation with trapping potential. The existence and blow-up behavior of solutions with normalized
In this paper, we are concerned with the existence and asymptotic behavior of traveling wave fronts in a modified vector-disease model. We establish the existence of traveling wave solutions for the modified vector-disease model without delay, then explore the existence of traveling fronts for the model with a special local delay convolution kernel by employing the geometric singular perturbation theory and the linear chain trick. Finally, we deal with the local stability of the steady states, the existence and asymptotic behaviors of traveling wave solutions for the model with the convolution kernel of a special non-local delay.
This work is concerned with the following nonautonomous evolutionary system on a Banach space
where
We investigate a quasi-linear parabolicproblem with nonlocal absorption, for which the comparison principle is not always available. Thesufficient conditions are established via energy method to guaranteesolution to blow up or not, and the long time behavior is alsocharacterized for global solutions.
In this paper, we prove some new local Aronson-Bénilan type gradient estimates for positive solutions of the porous medium equation
coupled with Ricci flow, assuming that the Ricci curvature is bounded. As application, the related Harnack inequality is derived. Our results generalize known results. These results may be regarded as the generalizations of the gradient estimates of Lu-Ni-Vázquez-Villani and Huang-Huang-Li to the Ricci flow.
In this article, we consider a class of fractional non-autonomous integro-differential evolution equation of Volterra type in a Banach space
In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators $L_K+V$ with nonnegative potentials $V∈ L^q_{\rm{loc}}(\mathbb{R}^n)$ for $q>\frac{n}{2s}$ with $0 < s < 1$ and $n>2s$; that is to say, we obtain the existence of a fundamental solution $\mathfrak{e}_V$ for $L_K+V$ satisfying
in the distribution sense, where $\delta _0$ denotes the Dirac delta mass at the origin. In addition, we obtain a decay of the fundamental solution $\mathfrak{e}_V$.
A comprehensive approach to Sobolev type embeddings, involving arbitrary rearrangement-invariant norms on the entire Euclidean space
The following coupled damped Klein-Gordon-Schrödinger equations are considered
where
Let
where
In this paper we study the existence, multiplicity and concentration behavior of solutions for the following critical fractional Schrödinger system
where
We relate the number of solutions with the topology of the set where the potentials
Sufficient and necessary conditions are presented for the order preservation of path-distribution dependent SDEs. Differently from the corresponding study of distribution independent SDEs, to investigate the necessity of order preservation for the present model we need to construct a family of probability spaces in terms of the ordered pair of initial distributions.
This note provides a counterexample to a proposition stated in [
We consider the bifurcation problem
where
In this paper, we consider the existence and exactness of multiple positive solutions for the nonlinear boundary value problem
where
In this paper, we focus on deriving traffic flow macroscopic models from microscopic models containing a local perturbation such as a traffic light. At the microscopic scale, we consider a first order model of the form "follow the leader" i.e. the velocity of each vehicle depends on the distance to the vehicle in front of it. We consider a local perturbation located at the origin that slows down the vehicles. At the macroscopic scale, we obtain an explicit Hamilton-Jacobi equation left and right of the origin and a junction condition at the origin (in the sense of [
This paper provides sufficient conditions for any map L, that is strongly piecewise linear relatively to a decomposition of
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