# American Institute of Mathematical Sciences

June  2004, 3(2): 175-182. doi: 10.3934/cpaa.2004.3.175

## Multiple positive periodic solutions for a delay host macroparasite model

 1 Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, United States

Received  May 2003 Revised  January 2003 Published  March 2004

A scalar non-autonomous periodic differential equation with delays arising from a delay host macroparasite model is studied. Two results are presented for the equation to have at least two positive periodic solutions: the hypotheses of the first result involve delays, while the second result holds for arbitrary delays.
Citation: Shangbing Ai. Multiple positive periodic solutions for a delay host macroparasite model. Communications on Pure & Applied Analysis, 2004, 3 (2) : 175-182. doi: 10.3934/cpaa.2004.3.175
 [1] Paolo Perfetti. Fixed point theorems in the Arnol'd model about instability of the action-variables in phase-space. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 379-391. doi: 10.3934/dcds.1998.4.379 [2] John R. Graef, Bo Yang. Multiple positive solutions to a three point third order boundary value problem. Conference Publications, 2005, 2005 (Special) : 337-344. doi: 10.3934/proc.2005.2005.337 [3] Roman Srzednicki. On periodic solutions in the Whitney's inverted pendulum problem. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 2127-2141. doi: 10.3934/dcdss.2019137 [4] Szandra Beretka, Gabriella Vas. Stable periodic solutions for Nazarenko's equation. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3257-3281. doi: 10.3934/cpaa.2020144 [5] Wojciech Kryszewski, Dorota Gabor, Jakub Siemianowski. The Krasnosel'skii formula for parabolic differential inclusions with state constraints. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 295-329. doi: 10.3934/dcdsb.2018021 [6] Aleksander Ćwiszewski, Piotr Kokocki. Krasnosel'skii type formula and translation along trajectories method for evolution equations. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 605-628. doi: 10.3934/dcds.2008.22.605 [7] Hasib Khan, Cemil Tunc, Aziz Khan. Green function's properties and existence theorems for nonlinear singular-delay-fractional differential equations. Discrete & Continuous Dynamical Systems - S, 2020, 13 (9) : 2475-2487. doi: 10.3934/dcdss.2020139 [8] Hiroshi Morishita, Eiji Yanagida, Shoji Yotsutani. Structure of positive radial solutions including singular solutions to Matukuma's equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 871-888. doi: 10.3934/cpaa.2005.4.871 [9] Parin Chaipunya, Poom Kumam. Fixed point theorems for cyclic operators with application in Fractional integral inclusions with delays. Conference Publications, 2015, 2015 (special) : 248-257. doi: 10.3934/proc.2015.0248 [10] Zengji Du, Xiao Chen, Zhaosheng Feng. Multiple positive periodic solutions to a predator-prey model with Leslie-Gower Holling-type II functional response and harvesting terms. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1203-1214. doi: 10.3934/dcdss.2014.7.1203 [11] Benjamin B. Kennedy. Multiple periodic solutions of state-dependent threshold delay equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1801-1833. doi: 10.3934/dcds.2012.32.1801 [12] Christopher M. Kellett. Classical converse theorems in Lyapunov's second method. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2333-2360. doi: 10.3934/dcdsb.2015.20.2333 [13] Lei Qiao. Matsaev's type theorems for solutions of the stationary Schrödinger equation and its applications. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5709-5720. doi: 10.3934/dcds.2016050 [14] Piotr Kokocki. Krasnosel'skii type formula and translation along trajectories method on the scale of fractional spaces. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2315-2334. doi: 10.3934/cpaa.2015.14.2315 [15] Najwa Najib, Norfifah Bachok, Norihan Md Arifin, Fadzilah Md Ali. Stability analysis of stagnation point flow in nanofluid over stretching/shrinking sheet with slip effect using buongiorno's model. Numerical Algebra, Control & Optimization, 2019, 9 (4) : 423-431. doi: 10.3934/naco.2019041 [16] Tiziana Cardinali, Paola Rubbioni. Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result. Discrete & Continuous Dynamical Systems - S, 2020, 13 (7) : 1947-1955. doi: 10.3934/dcdss.2020152 [17] Anna Cima, Armengol Gasull, Víctor Mañosa. Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 889-904. doi: 10.3934/dcds.2018038 [18] Juan Campos, Rafael Ortega. Location of fixed points and periodic solutions in the plane. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 517-523. doi: 10.3934/dcdsb.2008.9.517 [19] Weigao Ge, Li Zhang. Multiple periodic solutions of delay differential systems with $2k-1$ lags via variational approach. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4925-4943. doi: 10.3934/dcds.2016013 [20] Hans-Otto Walther. On Poisson's state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 365-379. doi: 10.3934/dcds.2013.33.365

2019 Impact Factor: 1.105