Existence results for a superlinear singular equation of Caffarelli-Kohn-Nirenberg type

In this paper, using Mountain Pass Lemma and Linking Argument, we prove the existence of nontrivial weak solutions for the Dirichlet problem for the superlinear equation of Caffarelli-Kohn-Nirenberg type in the case where the parameter $\lambda\in (0, \lambda_2)$, $\lambda_2$ is the second positive eigenvalue of the quasilinear elliptic equation of Caffarelli-Kohn-Nirenberg type.Comment: 13 pages, no figur

Existence results for a superlinear p-Laplacian equation with indeÿnite weights

Abstract In this paper, using Mountain Pass Lemma and Linking Argument, we prove the existence of nontrivial weak solutions for the Dirichlet problem of the superlinear p-Laplacian equation with indeÿnite weights in the case where the eigenvalue parameter ∈ (0; 2), 2 is the second positive eigenvalue of the p-Laplacian with indeÿnite weights.

Multiple stationary solutions to gkp equation in a bounded domain

In this paper, we study the existence of multiple stationarysolutions of Generalized Kadomtsev-Petviashvili (Abbr. GKP) equation in a bounded domain with smooth boundary and for superlinear nonlinear term f(u) = L|u|p-2u + |u|q-2u  where

Multiple solutions to P-Laplacian equation with singularity and cylindrical symmetry, Nonlinear Anal

Abstract In this paper, we shall investigate the existence of multiple (positive) weak solutions for the Dirichlet problem of the p-Laplacian with singularity and cylindrical symmetry. The results depends heavily on parameters n; p; q; r; s and ¿ 0. By the technical decomposition of the associated Nehari manifold into three parts + ; − and 0, and some compactness condition such as (PS) condition or local (PS) condition ((PS)c condition) at certain level of energy, we obtain two nonnegative minimizers of the energy functional on + and − , respectively.

The eigenvalue problem for a singular quasilinear elliptic equation

We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega)$ eigenfunction which is positive and unique (up to a multiplicative constant), that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue