Multiple Solutions for a Class ofN-Laplacian Equations with Critical Growth and Indefinite Weight

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

An existence results on positive solutions for a reaction-diffusion model with logistics growth and indefinite weight

In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...

Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth

In this paper‎, ‎we consider the following Kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$uin H^{1}(mathbb{R}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎The aim of this paper is to study the existence of positive ...

Multiplicity of solutions for p-Laplacian equation in R with indefinite weight

In this article, we study the existence of infinitely many nontrivial solutions for a class of superlinear p-Laplacian equations −∆pu+ V (x)|u| p−2 u = f(x, u), where the primitive of the nonlinearity f is of subcritical growth near ∞ in u and the weight function V is allowed to be sign-changing. Our results extend the recent results of Zhang and Xu [Q. Y. Zhang, B. Xu, Multiplicity of solution...