We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse
boundary value problems modeled by elliptic equations. We provide essentially optimal …

A new finite element method is presented that features the ability to include in the finite
element space knowledge about the partial differential equation being solved. This new …

Consider the problem-Art= f (~, u) on R. u20. LlfO on i-2.(1) u= o onaR where RC Rv is a
bounded domain with smooth boundary and f (_r, u): S2 x [0,=)+ R. We make the following …

LET G be a bounded open subset of lRN and 1< p< N. The main goal of this work is to study
the existence of a solution u to the following quasilinear equation i-div (] Du] p-ZDU)= a (x) …

In the present paper, we are concerned with a susceptible-infected-susceptible epidemic
reaction-diffusion model governed by a mass action infection mechanism and linear birth …

This paper is concerned with the existence and qualitative property of standing wave
solutions for the nonlinear Schrödinger equation with E being a critical frequency in the …

For elliptic equations of the form Δu-V(εx)u+f(u)=0,x∈\bfR^N, where the potential V satisfies
|x|→∞V(x)>\bfR^NV(x)=0, we develop a new variational approach to construct localized …

Surface area measures are local versions of quermassintegrals in the theory of convex
bodies. If the boundary of the convex body is smooth, the corresponding surface area …

In this paper we study the following coupled Schrödinger system, which can be seen as a
critically coupled perturbed Brezis–Nirenberg problem:\left {-Δ u+\lambda_1 u=\mu_1 u^ 3+ …

For elliptic equations ε 2 Δ u− V (x) u+ f (u)= 0, x∈ RN, N≧ 3, we develop a new variational
approach to construct localized positive solutions which concentrate at an isolated …