作者机构：
[Zhang, ZJ] Cent China Normal Univ, Dept Math, Lab Nonlinear Anal, Wuhan 430079, Peoples R China.;[Zhang, ZJ] Zhengzhou Inst Technol, Inst Chem Technol, Zhengzhou
通讯机构：
[Zhang, ZJ] C;Cent China Normal Univ, Dept Math, Lab Nonlinear Anal, Wuhan 430079, Peoples R China.
关键词：
Schrodinger equation;branch of solutions;bifurcation
摘要：
This paper studies the following semilinear Schrodinger problem -△u + v(x)u = λu - g(x)|u|p- 1u, x ∈ RN.It is proven that there exists a bifurcation branch of solutions for the above problem, when g(x) can possibly vanish except for a bounded domain Ω(∪) RN.
期刊：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY,2003年46(3):597-607 ISSN：0013-0915
通讯作者：
Kupper, T
作者机构：
Math Univ Koln, D-50923 Cologne, Germany.;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;Univ Manchester, Dept Math, Manchester M13 9PL, Lancs, England.;[Kupper, T] Math Univ Koln, Albertus Magnus Pl, D-50923 Cologne, Germany.
通讯机构：
[Kupper, T] M;Math Univ Koln, Albertus Magnus Pl, D-50923 Cologne, Germany.
摘要：
In this paper we study the existence of multiple positive solutions and the bifurcation problem for the following equation:\n$$ -\Delta u+u=\biggl(\int_{\mathbb{R}^3}\frac{|u(y)|^2}{|x-y|}\,\mathrm{d}y\biggr)u+\mu f(x),\quad x\in\mathbb{R}^3, $$\nwhere $f(x)\in H^{-1}(\mathbb{R}^3)$, $f(x)\geq0$, $f(x)\not\equiv0$. We show that there are positive constants $\mu^{*}$ and $\mu^{**}$ such that the above equation possesses at least two positive solutions for $\mu\in(0,\mu^{*})$, and no positive solution for $\mu>\mu^{**}$. Furthermore, we prove that $\mu=\mu^{*}$ is a bifurcation point for the equation under study.\nAMS 2000 Mathematics subject classification: Primary 35J60; 35J70
摘要：
In this paper, we consider the existence of solutions for the following equation: -Δu+u=(|u|2*1/|x|)u+g(x), x∈R3, where g(x)≥0, g(x)≢0, and g(x)∈H-1(R3). We prove that there exists a constant C, if ∥g(x)∥H-1≤C, there are at least two solutions of the equation.
摘要：
This paper considers the existence of solutions for the following problem: -Delta u + u + v(x)u = (\u\(2) (*) 1/\x\)u + g(x), x is an element of R-3 where v(x) be a continuous function on R-3,v(x) < 0, v(x) --> 0, (as \x\ -->1 infinity); g(x) greater than or equal to 0,g(x) not equivalent to 0 and g(x) is an element of H-1(R-3). The author proves that there exists a constant C, such that \\g(x)\\(H-1) less than or equal to C, then there are at least two solutions for the above problem.
