Positive least energy solutions for k-coupled Schrödinger system with critical exponent: the higher dimension and cooperative case

A nondegeneracy result for least energy solutions to a biharmonic problem with nearly critical exponent

Consider the problem ∆2u = c0K(x)uε , u > 0 in Ω, u = ∆u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN (N ≥ 5), c0 = (N − 4)(N − 2)N(N + 2), p = (N + 4)/(N − 4), pε = p− ε and K is a smooth positive function on Ω. Under some assumptions on the coefficient function K, which include the nondegeneracy of its unique maximum point as a critical point of HessK, we prove that least energy soluti...

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Positive solutions for coupled Schrödinger system with critical exponent in RN$\mathbb{R}^{N}$ (N≥5$N\geq5$)

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Solutions of an Elliptic System with a Nearly Critical Exponent

This problem has positive solutions for ǫ > 0 (with pqǫ > 1) and no non-trivial solution for ǫ ≤ 0. We study the asymptotic behaviour of least energy solutions as ǫ → 0. These solutions are shown to blow-up at exactly one point, and the location of this point is characterized. In addition, the shape and exact rates for blowing up are given. Résumé. Considéré le problème −∆uǫ = v p ǫ vǫ > 0 en Ω...