Nontrivial Periodic Solutions to Some Semilinear Sixth-Order Difference Equations

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

Existence and nonexistence of nontrivial solutions of semilinear sixth-order ordinary differential equations

K e y w o r d s E x t e n d e d Fisher-Kolmogorov equation, Sixth-order equations, Eigenvalue problems~ Clark's theorem, Variational methods. 1. I N T R O D U C T I O N Bistable systems play an important role in the study of spatial patterns. Recently, interest has turned to higher-order model equations involving bistable dynamics, such as the extended Fisher-Kolmogorov (EFK) equation Ou 0% 02u...

Multiple Nontrivial Solutions of Elliptic Semilinear Equations

We find multiple solutions for semilinear boundary value problems when the corresponding functional exhibits local splitting at zero.

Nontrivial Periodic Solutions of Some Volterra Integral Equations

I. Introductory Remarks. My main purpose in this paper is to prove a bifurcation theorem for nontrivial periodic solutions of a general system of Volterra integral equations. The motivation for considering this problem can be found in models which arise in population dynamics, epidemiology and economics [1,3,6], an example of which appears in §5. The approach taken is that which is usually refe...

Nontrivial solutions of elliptic semilinear equations at resonance

We find nontrivial solutions for semilinear boundary value problems having resonance both at zero and at infinity.