共查询到20条相似文献,搜索用时 15 毫秒
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The aim of this paper is to study the ground state solution for a Kirchhoff-type elliptic system without the Ambrosetti–Rabinowitz condition. 相似文献
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Yunfeng Wei Caisheng Chen Qiang Chen Hongwei Yang 《Mathematical Methods in the Applied Sciences》2020,43(1):320-333
In this article, we prove the Liouville-type theorem for stable solutions of weighted p-Laplace–type Grushin equations (1) and (2) where p ≥ 2, q>0 and are nonnegative functions satisfying and as ‖z‖G ≥ R0 with p−Nγ<b<θ+p, R0,Ci(i=1,2) are some positive constants. ∇G=(∇x,(1+γ)|x|γ∇y),γ ≥ 0, and The results hold true for Nγ<μ0(p,b,θ) in 1 and q>qc(p,Nγ,b,θ) in 2 . Here, μ0 and qc are new exponents, which are always larger than the classical critical ones and depend on the parameters p,b and θ. Nγ=N1+(1+γ)N2 is the homogeneous dimension of 相似文献
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Didier Smets 《Transactions of the American Mathematical Society》2005,357(7):2909-2938
We study a time-independent nonlinear Schrödinger equation with an attractive inverse square potential and a nonautonomous nonlinearity whose power is the critical Sobolev exponent. The problem shares a strong resemblance with the prescribed scalar curvature problem on the standard sphere. Particular attention is paid to the blow-up possibilities, i.e. the critical points at infinity of the corresponding variational problem. Due to the strong singularity in the potential, some new phenomenon appear. A complete existence result is obtained in dimension 4 using a detailed analysis of the gradient flow lines.
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We study the existence of positive solutions of a linear elliptic
equation with critical Sobolev exponent in a nonlinear Neumann boundary
condition. We prove a result which is similar to a classical result of Brezis
and Nirenberg who considered a corresponding problem with nonlinearity in
the equation. Our proof of the fact that the dimension three is critical uses
a new Pohoaev-type identity.AMS Subject Classification: Primary: 35J65; Secondary: 35B33. 相似文献
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In this article, we prove that semi-linear elliptic equations with critical cone Sobolev exponents possess a nodal solution. 相似文献
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In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory of genus, we obtain several results under different conditions. 相似文献
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Jianqing Chen 《Mathematische Nachrichten》2007,280(8):838-850
In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with Hardy–Sobolev critical growth and singular term by using variational methods. The result obtained here, even in a particular case, relates with a partial (positive) answer to an open problem proposed in: A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations 177 , 494–522 (2001). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
Dengfeng Lü 《Mathematical Methods in the Applied Sciences》2014,37(4):581-596
In the present paper, we deal with the existence and multiplicity of nontrivial solutions for a class of polyharmonic elliptic systems with Sobolev critical exponent in a bounded domain. Some new existence and multiplicity results are obtained. Our proofs are based on the Nehari manifold and Ljusternik–Schnirelmann theory. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Antonella Fiacca Nikolaos Matzakos Nikolaos S. Papageorgiou Raffaella Servadei 《Proceedings Mathematical Sciences》2001,111(4):489-508
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities.
First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is
defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between
them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed
by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This
case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that
the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity.
Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial
solutions (multiplicity theorem). 相似文献
19.
Let Ω be an open-bounded domain in RN(N?3) with smooth boundary ∂Ω. We are concerned with the multi-singular critical elliptic problem
20.
Jan Chabrowski 《Ricerche di matematica》2007,56(2):297-319
We consider the semilinear Neumann problem involving the critical Sobolev exponent with an indefinite weight function and
a concave purturbation. We prove the existence of two distinct solutions.
相似文献