共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
3.
Sabrine Gontara Syrine Masmoudi 《Journal of Mathematical Analysis and Applications》2010,369(2):719-934
Let Ω be a C1,1-bounded domain in Rn for n?2. In this paper, we are concerned with the asymptotic behavior of the unique positive classical solution to the singular boundary-value problem Δu+a(x)u−σ=0 in Ω, u|∂Ω=0, where σ?0, a is a nonnegative function in , 0<α<1 and there exists c>0 such that . Here λ?2, μk∈R, ω is a positive constant and δ(x)=dist(x,∂Ω). 相似文献
4.
5.
Tiexiang Li 《Journal of Mathematical Analysis and Applications》2010,369(1):245-257
In this paper, we study the decomposition of the Nehari manifold via the combination of concave and convex nonlinearities. Furthermore, we use this result and the Ljusternik-Schnirelmann category to prove that the existence of multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent. 相似文献
6.
Giovanni Anello 《Journal of Differential Equations》2007,234(1):80-90
In this paper we prove that if the potential has a suitable oscillating behavior in any neighborhood of the origin (respectively +∞), then under very mild conditions on the perturbation term g, for every k∈N there exists bk>0 such that
7.
We analyze blow-up phenomena of bounded integrable solutions of a semilinear fourth order elliptic problem with a large exponent
under Dirichlet boundary conditions. We extend the results obtained by Ren-Wei in [26] and [27] to the biharmonic case. 相似文献
8.
9.
In this paper, we consider a Dirichlet problem involving the p(x)-Laplacian of the type We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces. 相似文献
10.
11.
12.
Massimo Grossi 《Journal of Functional Analysis》2008,254(12):2995-3036
Let us consider the problem
(0.1) 相似文献
13.
Massimo Grossi 《Journal of Differential Equations》2008,245(10):2917-2938
Let us consider the problem
(0.1) 相似文献
14.
Gabriele Bonanno Nicola Giovannelli 《Journal of Mathematical Analysis and Applications》2005,308(2):596-604
A multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals. 相似文献
15.
Dirichlet problem with indefinite nonlinearities 总被引:2,自引:0,他引:2
Kung-Ching Chang Mei-Yue Jiang 《Calculus of Variations and Partial Differential Equations》2004,20(3):257-282
We consider the following nonlinear elliptic equation
in a bounded domain
with the Dirichlet boundary condition,
and
, g1(u)u and g2(u)u are positive for |u| > > 1. Some existence results are given for superlinear g1 and g2 via the Morse theory.Received: 16 Januray 2003, Accepted: 26 August 2003, Published online: 24 November 2003Mathematics Subject Classification (2000):
35J20, 35J25, 58E05Parts of the work were completed while the authors were visiting the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. The authors thank the hospitality of ICTP. Both authors are supported by NSFC, RFDP, MCME, the second author is also supported by the Foundation for University Key Teacher of the Ministry of Education of China and the 973 project of the Ministry of Science and Technology of China. 相似文献
16.
We consider a semilinear elliptic partial differential equation, depending on two positive parameters and , coupled with homogeneous Dirichlet boundary conditions. Assuming only one-sided growth conditions on the nonlinearities involved, we prove the existence of at least three weak solutions for and lying in convenient intervals. We employ techniques of nonsmooth analysis introduced by Degiovanni and Zani, and a theorem of Ricceri for multiplicity of local minimizers. 相似文献
17.
We study solutions of the Dirichlet problem for a second-order parabolic equation with variable coefficients in domains with nonsmooth lateral surface. The asymptotic expansion of the solution in powers of the parabolic distance is obtained in a neighborhood of a singular point of the boundary. The exponents in this expansion are poles of the resolvent of an operator pencil associated with the model problem obtained by freezing the coefficients at the singular point. The main point of the paper is in proving that the resolvent is meromorphic and in estimating it. In the one-dimensional case, the poles of the resolvent satisfy a transcendental equation and can be expressed via parabolic cylinder functions.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 12–23, January, 1996.This work was partially supported by the Russian Foundation for Basic Research under grant No. 242 93-01-16035. 相似文献
18.
We consider the boundary value problem Δu+up=0 in a bounded, smooth domain Ω in R2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Ω which ensure the existence of a positive solution up concentrating at exactly m points as p→∞. In particular, for a nonsimply connected domain such a solution exists for any given m?1. 相似文献
19.
In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic equation. With the help of the Nehari manifold and the center mass function, we prove that there are at least four positive solutions for a semilinear elliptic equation in a finite strip with a hole. 相似文献