Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters

On the Morse Indices of Sign Changing Solutions of Nonlinear Elliptic Problems

POSITIVE SOLUTIONS FOR SINGULAR THREE-POINT BOUNDARY-VALUE PROBLEMS WITH SIGN CHANGING NONLINEARITIES DEPENDING ON x′

Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem x′′(t) + a(t)f(t, x(t), x′(t)) = 0, 0 < t < 1, x′(0) = 0, x(1) = αx(η), where 0 < α < 1, 0 < η < 1, and f may change sign and may be singular at x = 0 and x′ = 0.

Superlinear elliptic problems with sign changing coefficients

Via variational methods, we study multiplicity of solutions for the problem    −∆u = λb(x)|u|q−2u + a u + g(x, u) in Ω , u = 0 on ∂Ω . where a simple example for g(x, u) is |u|p−2u; here a, λ are real parameters, 1 < q < 2 < p ≤ 2∗ and b(x) is a function in a suitable space L. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any λ > 0, and a...

Multiple Positive Solutions for Quasilinear Elliptic Problems with Sign-changing Nonlinearities

Using variational arguments we prove some nonexistence and multiplicity results for positive solutions of a system of p−Laplace equations of gradient form. Then we study a p−Laplace type problem with nonlinear boundary conditions.

Multiple Solutions and a Sign-Changing Solution for Semi-Linear Elliptic Problems with Resonance