Positive solutions for coupled Schrödinger system with critical exponent in RN$\mathbb{R}^{N}$ (N≥5$N\geq5$)
نویسندگان
چکیده
منابع مشابه
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 ...
متن کاملLinear Functions Preserving Sut-Majorization on RN
Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if t...
متن کاملGlobal existence for a coupled system of Schrödinger equations with power-type nonlinearities
u j : RN ×R → C, ψ j0 : RN → C for j = 1, 2, . . . , m and ajk = akj are positive real numbers. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of a vector-valued Gagliardo-Nirenberg inequality is deduced, which yields the minimal embedding constant for the inequality. Using this minimal embedding constant, global existence for small initial data is...
متن کاملUniqueness of Positive Solutions to Some Coupled Nonlinear Schrödinger Equations
We study the uniqueness of positive solutions of the following coupled nonlinear Schrödinger equations: ∆u1 − λ1u1 + μ1u1 + βu1u2 = 0 in RN , ∆u2 − λ2u2 + μ2u2 + βu1u2 = 0 in RN , u1 > 0, u2 > 0, u1, u2 ∈ H1(RN ) where N ≤ 3, λ1, λ2, μ1, μ2 are positive constants and β ≥ 0 is a coupling constant. We prove first the uniqueness of positive solution for sufficiently small β > 0. Secondly, ass...
متن کاملExistence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in R
Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in RN . These equations contain strongly singular nonlinearities which include derivatives of the second order. Such equations have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superf...
متن کامل