Search results for "homoclinic solution"

showing 3 items of 3 documents

Positive solutions of Dirichlet and homoclinic type for a class of singular equations

2018

Abstract We study a nonlinear singular boundary value problem and prove that, depending on a relationship between exponents of power terms, the problem has either solutions of Dirichlet type or homoclinic solutions. We make use of shooting techniques and lower and upper solutions.

Dirichlet problemPure mathematicsClass (set theory)SingularityApplied Mathematics010102 general mathematicsAnalysiType (model theory)01 natural sciencesDirichlet distributionPositive solution010101 applied mathematicssymbols.namesakeNonlinear systemSingularityHomoclinic solutionsymbolsHomoclinic orbitBoundary value problem0101 mathematicsAnalysisDirichlet problemMathematicsJournal of Mathematical Analysis and Applications
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Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition

2021

The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

Nonlinear systemCompact spaceSettore MAT/05 - Analisi MatematicaDifferential equationGeneral MathematicsMountain pass theoremMathematical analysisMathematics::Analysis of PDEsGeneral Physics and AstronomyHomoclinic orbitLaplace operator(p q)-Laplacian operator Difference equations homoclinic solutions non-zero solutionsMathematicsActa Mathematica Scientia
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A note on homoclinic solutions of (p,q)-Laplacian difference equations

2019

We prove the existence of at least two positive homoclinic solutions for a discrete boundary value problem of equations driven by the (p,q) -Laplace operator. The properties of the nonlinearity ensure that the energy functional, corresponding to the problem, satisfies a mountain pass geometry and a Palais–Smale compactness condition.

Pure mathematicsAlgebra and Number TheoryDifference equationApplied MathematicsOperator (physics)010102 general mathematicshomoclinic solution01 natural sciences010101 applied mathematicsNonlinear system(pq)-Laplace operatorpositive solutionSettore MAT/05 - Analisi MatematicaBoundary value problemHomoclinic orbitPalais–Smale condition0101 mathematicsLaplace operatorAnalysisMathematicsJournal of Difference Equations and Applications
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