共查询到20条相似文献,搜索用时 15 毫秒
1.
Norimichi Hirano 《Journal of Differential Equations》2009,247(5):1311-2003
Let N?3, 2*=2N/(N−2) and Ω⊂RN be a bounded domain with a smooth boundary ∂Ω and 0∈Ω. Our purpose in this paper is to consider the existence of solutions of Hénon equation:
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Variational methods are used to prove the existence of multiple positive and sign-changing solutions for a Schrödinger equation with singular potential having prescribed finitely many singular points. Some exact local behavior for positive solutions obtained here are also given. The interesting aspects are two. One is that one singular point of the potential V(x) and one positive solution can produce one sign-changing solution of the problem. The other is that each sign-changing solution changes its sign exactly once. 相似文献
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In this paper, under an improved Hardy-Rellich's inequality, we study the existence of multiple and sign-changing solutions for a biharmonic equation in unbounded domain by the minimax method and linking theorem. 相似文献
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Jianqing Chen Shujie Li Yongqing Li 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(3):453-474
Variational methods are used to prove the existence of positive and sign-changing solutions for a semilinear equation involving singular potential and critical exponent in any bounded domain.*supported in part by Tian Yuan Foundation of NNSF (A0324612)**Supported by 973 Chinese NSF and Foundation of Chinese Academy of Sciences.***Supported in part by NNSF of China.Received: September 23, 2002; revised: November 30, 2003 相似文献
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The main goal of this paper is to study the asymptotic expansion near the boundary of the large solutions of the equation
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Weihua Wang Aibin Zang Peihao Zhao 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4377-4385
We show that there exist at least three nontrivial solutions for a class of fourth elliptic equations under Navier boundary conditions by linking approaches. 相似文献
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Norimichi Hirano 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2580-2593
In this paper, we consider the multiple existence of sign changing solutions of coupled nonlinear Schrödinger equations
(P) 相似文献
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In this paper, one-dimensional (1D) nonlinear Schrödinger equation
iut−uxx+mu+4|u|u=0 相似文献
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We consider the Neumann problem for the Hénon equation. We obtain existence results and we analyze the symmetry properties of the ground state solutions. We prove that some symmetry and variational properties can be expressed in terms of eigenvalues of a Steklov problem. Applications are also given to extremals of certain trace inequalities. 相似文献
10.
Juncheng Wei Matthias Winter 《Calculus of Variations and Partial Differential Equations》2000,10(3):249-289
We study the Cahn-Hilliard equation in a bounded smooth domain without any symmetry assumptions. We prove that for any fixed
positive integer K there exist interior K–spike solutions whose peaks have maximal possible distance from the boundary and from one another. This implies that for
any bounded and smooth domain there exist interior K–peak solutions. The central ingredient of our analysis is the novel derivation and exploitation of a reduction of the energy
to finite dimensions (Lemma 5.5) with variables which are closely related to the location of the peaks. We do not assume nondegeneracy
of the points of maximal distance to the boundary but can do with a global condition instead which in many cases is weaker.
Received March 5, 1999 / Accepted June 11, 1999 相似文献
11.
Yanheng Ding 《Journal of Differential Equations》2010,249(5):1015-1034
We study the semi-classical limit of the least energy solutions to the nonlinear Dirac equation
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In this work we consider the first boundary value problem for a parabolic equation of second order with a small parameter on a half-axis (i.e., we consider the one-dimensional case). We take the zero initial condition. We construct the global (that is, the caustic points are taken into account) asymptotics of a solution for the boundary value problem. The asymptotic solution of this problem has a different structure depending on the sign of the coefficient (the drift coefficient) at the derivative of first order at a boundary point. The constructed asymptotic solutions are justified. 相似文献
16.
Bhatia Sumit Kaur 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2368-2382
Let Ω be a bounded domain in RN,N≥2, with C2 boundary. In this work, we study the existence of multiple positive solutions of the following problem:
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In this paper, we study the nonlinear stationary Schrödinger-Maxwell equations
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