Large and Small Solutions of a Class of Quasilinear Elliptic Eigenvalue Problems

A note on quasilinear elliptic eigenvalue problems

We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.

Quasilinear Elliptic Systems of Resonant Type and Nonlinear Eigenvalue Problems

Eigenvalue problems for a class of singular quasilinear elliptic equations in weighted spaces

Abstract: In this paper, by using the Galerkin method and the generalized Brouwer’s theorem, some problems of the higher eigenvalues are studied for a class of singular quasiliner elliptic equations in the weighted Sobolev spaces. The existence of weak solutions is obtained for this problem.

Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator

The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.

Eigenvalue Problems for a Quasilinear Elliptic Equation on Rn

where λ ∈ R. Next, we state the general hypotheses which will be assumed throughout the paper. (E) Assume that N , p satisfy the following relation N > p > 1. (G) g is a smooth function, at least C1,α(RN ) for some α∈ (0,1), such that g ∈ L∞(RN ) and g(x) > 0, on Ω+, with measure of Ω+, |Ω+| > 0. Also there exist R0 sufficiently large and k > 0 such that g(x) <−k, for all |x| > R0. Generally, p...