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1.
李工宝 《数学物理学报(B辑英文版)》1989,(2)
In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not be compact operators from E to R~1. 相似文献
2.
李工宝 《数学物理学报(B辑英文版)》1986,(1)
§0. Introduction This paper is devoted to discuss two classes of variational problems in certain Orlicz-Sobolev spaces. In the first part of the paper, we discuss a higher order problem in calculus of variations with strong nonlinearity. In [1], Prof. Ding Xiaxi, 相似文献
3.
该文研究椭圆型方程{-Δpu+m|u|p-2u-Δqu+n|u|q-2u=g(x,u),x∈RN,u∈ W1,p(RN)∩W1,q(RN)弱解在全空间RN上的衰减性,其中m,n≥0,N≥3,1
相似文献
4.
In this paper, we use the concentration-compactness prieciple togther with the Mountain Pass Lemma to get the existence of nontrivial solutions of the following scalar field equations with strong nonlinearity 相似文献
5.
李工宝 《数学物理学报(A辑)》1985,(4)
本文分两节讨论Orlica-Sobolev空间的两类变分问题。 第一节研究一类Orlica-Sobolev空间的强非线性高阶变分问题。丁夏畦教授等在[1]中研究了形如 相似文献
6.
In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrdinger-Kirchhoff type -εpMεp_N∫RN|▽u|p△pu+V(x)|u|p-2u=f(u) in R~N, where △_p is the p-Laplacian operator, 1 p N, M :R~+→R~+ and V :R~N→R~+are continuous functions,ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and LyusternikSchnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation. 相似文献
7.
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:{-△pu-△qu=│u│^p*-2u+μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^*=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ (0, μ0), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem. 相似文献
8.
该文研究椭圆型方程
{Δpu+m|u|p-2u-Δqu+n|u|q-2u=g(x, u), x∈RN,
u∈ W1, p(RN)∩W1, q(RN)
弱解在全空间RN上的衰减性, 其中m, n ≥ 0, N≥3, 1 < q < p < N, g(x, u)关于u满足类渐近线性. 证明了该方程的
弱解在无穷远处关于|x|呈指数衰减性. 相似文献
9.
In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations -(ε2a + εb∫R3|?u|2)?u + V(x)u = up, u > 0 in R3,which concentrate at non-degenerate critical points of the potential function V(x), where a, b >0, 1 < p < 5 are constants, and ε > 0 is a parameter. Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity, we establish the existe... 相似文献
10.
李工宝 《数学物理学报(B辑英文版)》1987,(4)
This paper shudies the existence of multiple critical points of perturbed symmetric functionals in W_0~(1,p)(Ω) (p≥2). For p>2, this kind of problems have never been studied befor and the main result of this paper generlizes the main results of [10]. 相似文献