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Positive homoclinic solutions of n‐th order difference equations with sign‐changing Green's function
Author(s) -
Cabada Alberto,
Dimitrov Nikolay D.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4929
Subject(s) - mathematics , sign (mathematics) , mathematical analysis , fixed point theorem , fixed point index , nonlinear system , constant (computer programming) , function (biology) , order (exchange) , homoclinic orbit , green's function , bifurcation , physics , finance , quantum mechanics , evolutionary biology , computer science , programming language , economics , biology , boundary value problem
In this paper we, consider an n‐th order nonlinear difference equation with parameter dependence. An exhaustive study of the related Green's function is done. The exact expression of the function is given. The range of parameter for which either it has constant sign or it changes sign is obtained. Some existence results for the nonlinear problem are deduced by using the classical Krasnosel'skii's fixed point theorem on cones and fixed point index theory.