共查询到20条相似文献,搜索用时 10 毫秒
1.
2.
Jing Zhang Shujie Li Yuwen Wang Xiaoping Xue 《Journal of Mathematical Analysis and Applications》2010,371(2):682-690
We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l>2 and (IIl), l?1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions. 相似文献
3.
In this paper, a semilinear elliptic equation with a nonlinear boundary condition and a perturbation in the reaction term is studied. The existence of a positive solution and another non-zero solution to the problem is proved when \(|\lambda |\) is small enough without any specific assumptions on the perturbation term. Moreover, it is shown that the non-zero solution becomes a positive one for small \(\lambda >0\) under suitable assumptions on the perturbation term. 相似文献
4.
5.
Two positive solutions are obtained for the nonlinear homogeneous system with nonlinear homogeneous boundary condition via the Nehari manifold approach. 相似文献
6.
7.
Positive entire solutions of semilinear elliptic equations 总被引:1,自引:0,他引:1
Nobuyoshi Fukagai 《Mathematische Annalen》1986,274(1):75-93
8.
We consider the existence of solutions to the semilinear elliptic problem
(∗)κ 相似文献
9.
The subject of nonnegative solutions for semilinear equationshas received considerable attention in recent years. A significantomission is the consideration of nonlinear boundary conditions,and their impact upon the structure of solutions. In this papersome such problems defined on spherically symmetric domainsare presented. The author considers the existence of radiallysymmetric solutions as a function of domain size, and also showsthat infinitesimal symmetry-breaking bifurcations may occurin the simplest eigenmode. This is precluded in the case ofhomogeneous Neumann or Dirichlet problems for similar sourceterms. Given the importance of robust simple symmetry-breaking(in cell division for example), this result suggests attentionshould be further focused upon modelling nonlinear boundaryconditions. 相似文献
10.
11.
12.
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
13.
14.
15.
16.
Positivity - We consider a nonlinear nonparametric elliptic Dirichlet problem driven by the p-Laplacian and reaction containing a singular term and a $$(p-1)$$ -superlinear perturbation. Using... 相似文献
17.
This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f. 相似文献
18.
For n≥3 and p>1, the elliptic equation Δu+K(x)up+μf(x)=0 in possesses a continuum of positive entire solutions, provided that (i) locally Hölder continuous functions K and f vanish rapidly, for instance, K(x),f(x)=O(|x|l) near ∞ for some l<−2 and (ii) μ≥0 is sufficiently small. Especially, in the radial case with K(x)=k(|x|) and f(x)=g(|x|) for some appropriate functions k,g on [0,∞), there exist two intervals Iμ,1, Iμ,2 such that for each α∈Iμ,1 the equation has a positive entire solution uα with uα(0)=α which converges to l∈Iμ,2 at ∞, and uα1<uα2 for any α1<α2 in Iμ,1. Moreover, the map α to l is one-to-one and onto from Iμ,1 to Iμ,2. If K≥0, each solution regarded as a steady state for the corresponding parabolic equation is stable in the uniform norm; moreover, in the radial case the solutions are also weakly asymptotically stable in the weighted uniform norm with weight function |x|n−2. 相似文献
19.
Large solutions of semilinear elliptic equations under the Keller-Osserman condition 总被引:1,自引:0,他引:1
Alan V. Lair 《Journal of Mathematical Analysis and Applications》2007,328(2):1247-1254
We consider the equation Δu=p(x)f(u) where p is a nonnegative nontrivial continuous function and f is continuous and nondecreasing on [0,∞), satisfies f(0)=0, f(s)>0 for s>0 and the Keller-Osserman condition where . We establish conditions on the function p that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of the given equation. 相似文献