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Abstract The main purpose of this paper is to analyze the asymptotic behaviour of the ground state solution of Henon equation −Δu=|x|αup−1 in Ω , u=0 on ∂Ω ( Ω⊂R n is a ball centered at the origin).… Expand
In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: −Δpu=|u|p⁎−2u+μ|u|p−2uin Ω,u=0on ∂Ω, provided N>p2+p, where… Expand
Abstract In this paper, we answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋0 be an open-bounded domain, Ω⊂R N (N⩾5) and… Expand
Let Ω⊂RN be a bounded domain such that 0∈Ω,N⩾7,2∗=2NN−2. We obtain existence of sign-changing solutions for the Dirichlet problem −Δu=μu|x|2+|u|2∗−2u+λu on Ω,u=0 on ∂Ω for suitable positive numbers μ… Expand
Abstract In this paper, we are concerned with the existence and uniqueness of multi-bump bound states of the nonlinear Schrodinger equations with electromagnetic potential i ℏ ∂ ψ ∂ t = ℏ i ∇ - A ( x… Expand
In this paper, we study the existence of multiple solutions of nonlinear elliptic problems in an exterior domain with Neumann boundary conditions.
Abstract In this paper, we present a new scheme to study the dynamics of a stochastic reaction–diffusion equation with the nonlinearity satisfying a dissipative condition with polynomial growth of… Expand
In this paper we study the existence and qualitative property of standing wave solutions ψ(x,t)=e−iEtℏu(x) for the nonlinear Schrodinger equation iℏ∂ψ∂t+ℏ22mΔψ−W(x)ψ+|ψ|p−1ψ=0 with E being a critical… Expand
AbstractIn this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by… Expand