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1.
MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT   总被引:1,自引:0,他引:1  
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
2.
We use the blow-up method to get the C~(1,α) partial regularity results for the following elliptic systems satisfying natural growth conditions:  相似文献
3.
In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem with natural growth conditions.  相似文献
4.
In this paper, we study the following eigenvalue problem involving limiting nonlinearity by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the known result in the positive mass case in the sense of seeking a nontrivial solution of the above eigenvalue problem.  相似文献
5.
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
6.
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
7.
In this paper, We get the existence of non-trivial solutions of the following elliptic equations where n>p≥2 and p~x=np/n-p.  相似文献
8.
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
9.
§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
10.
1 IntroductionIll tllis paper, we co1lsid(tr the fOllowillg elliptic prol)leInwllere n is a bOui1ded regular domai1l in RN(N > 3), N > p > 1, aild a: n - R is a Holdercontinuou8 function which chauges 8ign o11 fl so that the open setsandO-- = {z E Ola(z) < 0}are both nonemPty.We use the standard notations. Let II' lI, denote the norm of L'(o) for s21. DenoteW0lP(fl) the comPletion of C7(fl) under the norm IIuIl = llVuIl;, the norm of tlle dual spaceof WJlp(fl) will be denoted by Il…  相似文献
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