Sign Changing Solutions for Quasilinear Superlinear Elliptic Problems

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.

A Note on Additional Properties of Sign Changing Solutions to Superlinear Elliptic Equations

We obtain upper bounds for the number of nodal domains of sign changing solutions of semilinear elliptic Dirichlet problems using suitable min-max descriptions. These are consequences of a generalization of Courant’s nodal domain theorem. The solutions need not to be isolated. We also obtain information on the Morse index of solutions and the location of suband supersolutions.

Multiplicity of solutions for quasilinear elliptic boundary-value problems

This paper is concerned with the existence of multiple solutions to the boundary-value problem −(φp(u )) = λφq(u) + f(u) in (0, 1) , u(0) = u(1) = 0 , where p, q > 1, φx(y) = |y| y, λ is a real parameter, and f is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.

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