In this paper, we study the existence and multiplicity of positive solutions for semi-linear elliptic equations with a sign-changing weight function in weighted Sobolev spaces. By investigating the compact embedding theorem and based on the extraction of the Palais-Smale sequence in the Nehari manifold which is a subset of the weighted Sobolev spaces, we derive the existence of the multiple pos...

We investigate non-existence of non-negative dead core solutions for the problem [Formula: see text] Here, is a bounded smooth domain, fully nonlinear elliptic operator, sign-changing weight, text], and text]. show that this has no nontrivial if either close enough to or negative part sufficiently small. In addition, we obtain existence uniqueness positive solution under these conditions on Our...

in the paper we establish some new results depending on thecomparative growth properties of composition of entire functionsusing relative $l^{ast }$-order (relative $l^{ast }$-lowerorder) as compared to their corresponding left and right factorswhere $lequiv lleft( rright) $ is a slowly changing function.

In this paper, the relationships between sign-changing critical point theorems and the linking type theorems of M. Schechter and the saddle point theorems of P. Rabinowitz are established. The abstract results are applied to the study of the existence of sign-changing solutions for the nonlinear Schrödinger equation −∆u+V (x)u = f(x, u), u ∈ H1(RN ), where f(x, u) is a Carathéodory function. Pr...