Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients
Yuhua Long
Abstract
In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.
Topics & Concepts
MathematicsSign (mathematics)Nonlinear systemInvariant (physics)Mathematical analysisOrder (exchange)Series (stratigraphy)Periodic boundary conditionsBoundary value problemApplied mathematicsMathematical physicsPaleontologyEconomicsQuantum mechanicsBiologyPhysicsFinanceMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods