Boundary value problems with jumping nonlinearities

An Existence Result for a Class of Quasilinear Elliptic Boundary Value Problems with Jumping Nonlinearities

We establish an existence result for a class of quasilinear elliptic boundary value problems with jumping nonlinearities using variational arguments. First we calculate certain homotopy groups of sublevel sets of the asymptotic part of the variational functional. Then we use these groups to show that the full functional admits a linking geometry and hence a minmax critical point.

p-LAPLACIAN PROBLEMS WITH JUMPING NONLINEARITIES

We consider the p-Laplacian boundary value problem −(φp(u(x)) = f(x, u(x), u′(x)), a.e. x ∈ (0, 1), (1) c00u(0) + c01u ′(0) = 0, c10u(1) + c11u ′(1) = 0, (2) where p > 1 is a fixed number, φp(s) = |s|p−2s, s ∈ R, and for each j = 0, 1, |cj0|+ |cj1| > 0. The function f : [0, 1]× R2 → R is a Carathéodory function satisfying, for (x, s, t) ∈ [0, 1]× R2, ψ±(x)φp(s)− E(x, s, t) ≤ f(x, s, t) ≤ Ψ±(x)φ...

Higher Order Multi-point Boundary Value Problems with Sign-changing Nonlinearities and Nonhomogeneous Boundary Conditions

Abstract. We study classes of nth order boundary value problems consisting of an equation having a sign-changing nonlinearity f(t, x) together with several different sets of nonhomogeneous multi-point boundary conditions. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. Conditions are determined b...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Nonresonance Conditions for Generalised Φ-laplacian Problems with Jumping Nonlinearities

We consider the boundary value problem −ψ(x, u(x), u′(x))′ = f(x, u(x), u′(x)), a.e. x ∈ (0, 1), (1) c00u(0) = c01u ′(0), c10u(1) = c11u ′(1), (2) where |cj0| + |cj1| > 0, for each j = 0, 1, and ψ, f : [0, 1] × R2 → R are Carathéodory functions, with suitable additional properties. The differential operator generated by the left-hand side of (1), together with the boundary conditions (2), is a ...