共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we consider the elliptic equations with critical Sobolev exponents and multi-polar potentials in bounded symmetric domains and prove the existence and multiplicity of symmetric positive solutions by using the Ekeland variational principle and the Lusternik–Schnirelmann category theory. 相似文献
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Li Wang 《Journal of Mathematical Analysis and Applications》2011,383(2):541-552
In this paper, a singular elliptic system involving multiple critical exponents and the Caffarelli-Kohn-Nirenberg inequality is investigated. By using the extremals of the best Hardy-Sobolev constants, the existence and multiplicity of positive solutions to the system are established. 相似文献
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In this paper, we consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in RN, N?4, , is the critical Sobolev exponent, K(x) is a continuous function. When Ω and K(x) are invariant under a group of orthogonal transformations, we prove the existence of nodal and positive solutions for 0<λ<λ1, where λ1 is the first Dirichlet eigenvalue of on Ω. 相似文献
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Kuan-Ju Chen 《Journal of Mathematical Analysis and Applications》2006,319(2):841-862
In this paper, we study the existence of positive solutions of some nonlinear elliptic problems in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. 相似文献
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Smail Djebali 《Journal of Mathematical Analysis and Applications》2007,333(2):863-870
In this note we investigate the existence of positive solutions vanishing at +∞ to the elliptic equation Δu+f(x,u)+g(|x|)x⋅∇u=0, |x|>A>0, in Rn (n?3) under mild restrictions on the functions f, g. 相似文献
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Chang-Mu Chu Chun-Lei Tang 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5118-5130
In this paper, we study the existence and multiplicity of positive solutions to the following system , in Ω; u,v>0 in Ω; and u=v=0 on ∂Ω, where Ω is a bounded smooth domain in RN; FC1((R+)2,R+) is positively homogeneous of degree μ; ; and ε is a positive parameter. Using sub–supersolution method, we prove the existence of positive solutions for the above problem. By means of the variational approach, we prove the multiplicity of positive solutions for the above problem with μ(2,2*]. 相似文献
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Qiu-yi DAI~ 《中国科学A辑(英文版)》2007,50(8):1141-1156
This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained. 相似文献
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Jiqin Deng 《Journal of Mathematical Analysis and Applications》2007,332(1):475-486
In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of Schrödinger equations in two-dimensional exterior domains. 相似文献
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Jiqin Deng 《Journal of Mathematical Analysis and Applications》2007,336(2):1395-1405
In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of semilinear elliptic equations in exterior domain of Rn, n?3. 相似文献
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Radu Precup 《Journal of Mathematical Analysis and Applications》2009,352(1):48-56
Existence, localization and multiplicity results of positive solutions to a system of singular second-order differential equations are established by means of the vector version of Krasnoselskii's cone fixed point theorem. The results are then applied for positive radial solutions to semilinear elliptic systems. 相似文献
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Large solutions of semilinear elliptic equations under the Keller-Osserman condition 总被引:1,自引:0,他引:1
Alan V. Lair 《Journal of Mathematical Analysis and Applications》2007,328(2):1247-1254
We consider the equation Δu=p(x)f(u) where p is a nonnegative nontrivial continuous function and f is continuous and nondecreasing on [0,∞), satisfies f(0)=0, f(s)>0 for s>0 and the Keller-Osserman condition where . We establish conditions on the function p that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of the given equation. 相似文献
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Peng Feng 《Journal of Mathematical Analysis and Applications》2009,356(2):393-1788
In this paper, we show existence, uniqueness and exact asymptotic behavior of solutions near the boundary to a class of semilinear elliptic equations −Δu=λg(u)−b(x)f(u) in Ω, where λ is a real number, b(x)>0 in Ω and vanishes on ∂Ω. The special feature is to consider g(u) and f(u) to be regularly varying at infinity and b(x) is vanishing on the boundary with a more general rate function. The vanishing rate of b(x) determines the exact blow-up rate of the large solutions. And the exact blow-up rate allows us to obtain the uniqueness result. 相似文献
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We consider the semilinear elliptic equation Δu+K(|x|)up=0 in RN for N>2 and p>1, and study separation phenomena of positive radial solutions. With respect to intersection and separation, we establish a classification of the solution structures, and investigate the structures of intersection, partial separation and separation. As a consequence, we obtain the existence of positive solutions with slow decay when the oscillation of the function r−?K(r) with ?>−2 around a positive constant is small near r=∞ and p is sufficiently large. Moreover, if the assumptions hold in the whole space, the equation has the structure of separation and possesses a singular solution as the upper limit of regular solutions. We also reveal that the equation changes its nature drastically across a critical exponent pc which is determined by N and the order of the behavior of K(r) as r=|x|→0 and ∞. In order to understand how subtle the structure is on K at p=pc, we explain the criticality in a similar way as done by Ding and Ni (1985) [6] for the critical Sobolev exponent p=(N+2)/(N−2). 相似文献
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Zhou Wen-Shu 《Journal of Mathematical Analysis and Applications》2008,346(1):107-119
In this paper we study existence and multiplicity of weak solutions of the homogenous Dirichlet problem for a singular semilinear elliptic equation with a quadratic gradient term. The proofs for the main results are based on a priori estimates of solutions of approximate problems. 相似文献
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Giovanna Citti 《Annali di Matematica Pura ed Applicata》1991,158(1):315-330
Sunto Viene provato un teorema di esistenza di soluzioni positive per una certa classe di equazioni quasilineari ellittiche degeneri su aperti non limitati di Rn utilizzando un metodo di confronta all'infinito. 相似文献
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In this paper we find some new conditions to ensure the existence of infinitely many nontrivial solutions for the Dirichlet boundary value problems of the form −Δu+a(x)u=g(x,u) in a bounded smooth domain. Conditions (S1)–(S3) in the present paper are somewhat weaker than the famous Ambrosetti–Rabinowitz-type superquadratic condition. Here, we assume that the primitive of the nonlinearity g is either asymptotically quadratic or superquadratic as |u|→∞. 相似文献