共查询到20条相似文献,搜索用时 15 毫秒
1.
Lei Wei 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1739-1746
In this work, we consider semilinear elliptic equations with boundary blow-up whose nonlinearities involve a negative exponent. Combining sub- and super-solution arguments, comparison principles and topological degree theory, we establish the existence of large solutions. Furthermore, we show the existence of a maximal large positive solution. 相似文献
2.
We show that for ε small, there are arbitrarily many nodal solutions for the following nonlinear elliptic Neumann problem where Ω is a bounded and smooth domain in ℝ2 and f grows superlinearly. (A typical f(u) is f(u)= a1 u+p – a1 u-p, a1, a2 >0, p, q>1.) More precisely, for any positive integer K, there exists εK>0 such that for 0<ε<εK, the above problem has a nodal solution with K positive local maximum points and K negative local minimum points. This solution has at least K+1 nodal domains. The locations of the maximum and minimum points are related to the mean curvature on ∂Ω. The solutions are constructed as critical points of some finite dimensional reduced energy functional. No assumption on the symmetry, nor the geometry, nor the topology of the domain is needed. 相似文献
3.
4.
An elliptic system is considered in a smooth bounded domain, subject to Dirichlet boundary conditions of three different types. Based on the construction of certain upper and sub-solutions, we obtain some conditions on the parameters ai,bi,ci (i=1,2) and the exponents m,n,p,q to ensure the existence of positive solutions. Furthermore, uniqueness and boundary behavior of positive solutions is also discussed. 相似文献
5.
Summary We give sufficient conditions for the existence of positive solutions to some semilinear elliptic equations in unbounded Lipschitz domainsD
d
(d3), having compact boundary, with nonlinear Neumann boundary conditions on the boundary ofD. For this we use an implicit probabilistic representation, Schauder's fixed point theorem, and a recently proved Sobolev inequality forW
1,2(D). Special cases include equations arising from the study of pattern formation in various models in mathematical biology and from problems in geometry concerning the conformal deformation of metrics.Research supported in part by NSF Grants DMS 8657483 and GER 9023335This article was processed by the authors using the
style filepljourlm from Springer-Verlag. 相似文献
6.
7.
J. Chabrowski 《Journal of Fixed Point Theory and Applications》2007,2(2):333-352
We investigate the solvability of the Neumann problem involving the critical Sobolev exponent, the Hardy potential and a nonlinear
term of lower order. Lower order terms are allowed to interfere with the spectrum of the operator subject to the Neumann boundary conditions. Solutions are obtained via a min-max procedure based on the variational mountain-pass
principle and topological linking.
相似文献
8.
This paper is contributed to the Cauchy problem
9.
Vasilii V. Kurta 《Archiv der Mathematik》2006,87(4):368-374
We generalize and improve recent non-existence results for global solutions to the Cauchy problem for the inequality
as well as for the equation ut = Δu + |u|q in the half-space
.
Received: 16 September 2005 相似文献
10.
11.
We consider the blowup rate of solutions for a semilinear heat equation
12.
We study the long-time behavior of solutions of semilinear parabolic equation of the following type t∂u−Δu+a0(x)uq=0 where , d0>0, 1>q>0, and ω is a positive continuous radial function. We give a Dini-like condition on the function ω by two different methods which implies that any solution of the above equation vanishes in a finite time. The first one is a variant of a local energy method and the second one is derived from semi-classical limits of some Schrödinger operators. 相似文献
13.
Changshou Lin Liping Wang Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2007,30(2):153-182
We consider the following critical elliptic Neumann problem on , Ω; being a smooth bounded domain in is a large number. We show that at a positive nondegenerate local minimum point Q
0 of the mean curvature (we may assume that Q
0 = 0 and the unit normal at Q
0 is − e
N
) for any fixed integer K ≥ 2, there exists a μ
K
> 0 such that for μ > μ
K
, the above problem has K−bubble solution u
μ concentrating at the same point Q
0. More precisely, we show that u
μ has K local maximum points Q
1μ, ... , Q
K
μ ∈∂Ω with the property that and approach an optimal configuration of the following functional
(*) Find out the optimal configuration that minimizes the following functional: where are two generic constants and φ (Q) = Q
T
G
Q with G = (∇
ij
H(Q
0)).
Research supported in part by an Earmarked Grant from RGC of HK. 相似文献
14.
15.
Massimo Grossi Angela Pistoia Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2000,11(2):143-175
We study a perturbed semilinear problem with Neumann boundary condition
where is a bounded smooth domain of , , , if or if and is the unit outward normal at the boundary of . We show that for any fixed positive integer K any “suitable” critical point of the function
generates a family of multiple interior spike solutions, whose local maximum points tend to as tends to zero.
Received March 7, 1999 / Accepted October 1, 1999 / Published online April 6, 2000 相似文献
16.
We consider the stationary Gierer-Meinhardt system in a ball of RN:
17.
The main goal of this paper is to study the asymptotic expansion near the boundary of the large solutions of the equation
18.
19.
Layered solutions for a semilinear elliptic system in a ball 总被引:1,自引:0,他引:1
We consider the following system of Schrödinger-Poisson equations in the unit ball B1 of R3: