Nontrivial solutions of discrete Kirchhoff-type problems via Morse theory
Yuhua Long
Abstract
Abstract In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on the existence of nontrivial solutions by combining variational method with Morse theory. Several examples are provided to illustrate applications of our results.
Topics & Concepts
Morse theoryType (biology)MathematicsInfinityMorse codeZero (linguistics)Nonlinear systemMathematical analysisSeries (stratigraphy)Applied mathematicsComputer sciencePhysicsQuantum mechanicsBiologyPaleontologyPhilosophyEcologyLinguisticsTelecommunicationsAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsStability and Controllability of Differential Equations