Three Nontrivial Solutions for Second-Order Partial Difference Equation via Morse Theory
Yuhua Long, Huan Zhang
Abstract
In the present paper, we consider a second-order nonlinear partial difference equation with Dirichlet boundary conditions. Applying variational method together with the Morse theory, we establish a criterion to obtain at least three nontrivial solutions. An example is also elaborated to demonstrate our main result.
Topics & Concepts
Morse theoryMathematicsDirichlet distributionOrder (exchange)Boundary (topology)Dirichlet boundary conditionNonlinear systemMorse codeMathematical analysisBoundary value problemPartial differential equationApplied mathematicsPhysicsComputer scienceFinanceQuantum mechanicsEconomicsTelecommunicationsNonlinear Partial Differential EquationsDifferential Equations and Numerical MethodsNonlinear Differential Equations Analysis