An eigenvalue problem involving a degenerate and singular elliptic operator

An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term

In this paper we study a Dirichlet problem for an elliptic equation with degenerate coercivity and a singular lower order term with natural growth with respect to the gradient. The model problem is

ON AN EIGENVALUE PROBLEM INVOLVING THE p(x)–LAPLACE OPERATOR PLUS A NON–LOCAL TERM

We study an eigenvalue problem involving variable exponent growth conditions and a non-local term, on a bounded domain Ω ⊂ RN . Using adequate variational techniques, mainly based on the mountain-pass theorem of A. Ambrosetti and P. H. Rabinowitz, we prove the existence of a continuous family of eigenvalues lying in a neighborhood at the right of the origin. Mathematics subject classification (...

An Eigenvalue Problem for Elliptic Systems

By means of non-smooth critical point theory we prove existence of weak solutions for a general nonlinear elliptic eigenvalue problem under natural growth conditions .

Degenerate elliptic equations with singular nonlinearities

The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of RN , and compactness holds below a critical dimension N #. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p = 2 it is crucial to...

On an Inverse Eigenvalue Problem for a Semilinear Sturmäliouville Operator