On ground state and nodal solutions of Schrödinger–Poisson equations with critical growth

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.

Nodal Solutions of Elliptic Equations with Critical Sobolev Exponents

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 ...

critical period effects in foreign language learning:the influence of maturational state on the acquisition of reading,writing, and grammar in english as a foreign language

since the 1960s the age effects on learning both first and second language have been explored by many linguists and applied linguists (e.g lennerberg, 1967; schachter, 1996; long, 1990) and the existence of critical period for language acquisition was found to be a common ground of all these studies. in spite of some common findings, some issues about the impacts of age on acquiring a second or...

Solutions for Singular Critical Growth Schrödinger Equations with Magnetic Field

In this paper, we are concerned with the semilinear Schrödinger equation (1.1) −∆Au− V (x)u = |u| ∗−2u , x ∈ R , where −∆A = (−i∇+A)2, u : R → C, N ≥ 3, 2∗ = 2N N−2 denotes the critical Sobolev exponent, A = (A1, A2, ..., AN ) : R N → R is the vector (or magnetic) potential, the coefficient V is the scalar (or electric) potential and may be signchanging. The nonlinear Schrödinger equation arise...