共查询到20条相似文献,搜索用时 359 毫秒
1.
Jayne Thompson 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):4989-4999
We establish stability and nonstability results for a domain-wall brane model arising in classical field theory. In particular, we show the nonexistence of nontrivial bounded solutions on the real line for a coupled pair of parameter dependent linear second order ordinary differential equations for an open set of those parameters. Moreover, we establish the existence of nontrivial solutions for a hypersurface of the parameters. We use Fredholm theory for compact linear operators combined with the Lyapunov-Schmidt method to prove our results. The model is stable, respectively unstable, for those parameters for which the coupled system does not, respectively does, have nontrivial solutions. 相似文献
2.
In this paper, we study existence and multiplicity of nontrivial solutions for a class of Schrödinger–Maxwell systems via variational methods. Some new existence results of nontrivial solutions are obtained. 相似文献
3.
A periodic predator–prey-chain system with impulsive effects is considered. By using the global results of Rabinowitz and standard techniques of bifurcation theory, the existence of its trivial, semi-trivial and nontrivial positive periodic solutions is obtained. It is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi-trivial periodic solution. Furthermore, the stability of these periodic solutions is studied. 相似文献
4.
Dengfeng Lü 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6371-6382
In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with Sobolev critical exponent in a bounded domain. By using the variational method and the Nehari manifold, we obtain the existence and multiplicity results of nontrivial solutions for the systems. 相似文献
5.
In this paper, Fucik spectrum, ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear
elliptic boundary value problems with jumping nonlinearities at zero or infinity, and some new results on the existence of
nontrivial solutions, multiple solutions and sign-changing solutions are obtained. In one case seven nontrivial solutions
are got. The techniques have independent interest. 相似文献
6.
Shiwang Ma Zhi-Qiang Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(5):1413-1442
In this paper, we study the existence of multibump solutions for discrete nonlinear Schrödinger equations with periodic potentials. We first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group. Then, we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear Schrödinger equations, and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case. As an application, we get, without any symmetry assumptions, infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity. 相似文献
7.
8.
杨志林 《数学物理学报(A辑)》2006,26(2):233-240
该文利用拓扑方法和锥理论研究下列Hammerstein非线性积分方程组u(x)=∫G k(x,y)f(y,u(y),v(y)) dy,v(x)=∫Gk(x,y)g(y,u(y),v(y)) dy.在适当的条件下,证明了上述方程组非平解的存在性,并把所得结果应用于研究非线性二阶常微分方程组边值问题的非平凡解的存在性. 相似文献
9.
本文研究一类具有次临界多项式增长或次临界指数型(临界指数型)增长的(p,2)-拉普拉斯方程一个正解及无穷多非平凡解的存在性,运用山路定理及喷泉定理,得到了拉普拉斯方程非平凡解的一些存在性结果. 相似文献
10.
Lingju Kong 《中国科学 数学(英文版)》2019,(7)
We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived; in particular, the existence of at lease two distinct nontrivial non-negative solutions is established for a scalar degenerate problem. One example is provided to show the applicability of our results. 相似文献
11.
研究了一类具有非光滑局部Lipschitz位势(半变分不等式)的非线性特征值问题其中1
相似文献
12.
本文论讨了三个问题:①二阶非线性微分方程的初值问题;②运用非线性算子证明了非平凡解的存在性和唯一性;③给出了一个非负非平凡解的估计式. 相似文献
13.
本文研究了一类含临界指数的p-Kirchhoff型方程.利用变分方法与集中紧性原理,通过证明对应的能量泛函满足局部的(PS)_c条件,得到了这类方程非平凡解的存在性,推广了关于Kirchhoff型方程的相关结果. 相似文献
14.
《Mathematical Methods in the Applied Sciences》2018,41(8):3197-3212
In this paper, the existence and multiplicity of nontrivial solutions are obtained for nonlinear fractional differential systems with p‐Laplacian by combining the properties of fractional calculus with critical point theory. Firstly, we present a result that a class of p‐Laplacian fractional differential systems exists infinitely many solutions under the famous Ambrosetti‐Rabinowitz condition. Then, a criterion is given to guarantee that the fractional systems exist at least 1 nontrivial solution without satisfying Ambrosetti‐Rabinowitz condition. Our results generalize some existing results in the literature. 相似文献
15.
J. P. Keener 《Studies in Applied Mathematics》1976,55(3):187-211
A set of two coupled nonlinear diffusion reaction equations is studied and the existence of secondary bifurcation is shown. Using the method of two-timing, it is found that diffusion reaction equations of this type can exhibit an exchange of stability between distinct nontrivial solutions. This exchange can provide either a smooth or discontinuous transition between stable solutions, and the nontrivial solutions can be either steady or temporally periodic. This analysis is applied to the model biochemical reaction of Prigogine and the types of secondary bifurcation which occur in this model are classified. 相似文献
16.
A. Pankov 《Milan Journal of Mathematics》2005,73(1):259-287
We present some results on existence of nontrivial solutions of periodic stationary nonlinear Schr?dinger equations. We also
sketch an application to nonlinear optics and discuss some open problems.
Received: December 2004 相似文献
17.
The Perron effect is the effect in which the characteristic Lyapunov exponents of solutions of a differential system change
sign from negative to positive when passing to a perturbed system. We show that this effect is realized on all nontrivial
solutions of two two-dimensional systems: an original linear system with negative characteristic exponents and a perturbed
system with small perturbations of arbitrary order m > 1 in a neighborhood of the origin, all of whose nontrivial solutions have positive characteristic exponents. We compute
the exact positive value of the characteristic exponents of solutions of the two-dimensional nonlinear Perron system with
small second-order perturbations, which realizes only a partial Perron effect. 相似文献
18.
Gianni Arioli 《Journal of Differential Equations》2007,235(1):298-307
We study a reaction-diffusion system of two parabolic differential equations describing the behavior of a nuclear reactor. We provide existence results for nontrivial periodic solutions, nonexistence results for stationary solutions and we prove that, depending on the value of the parameters, either the system admits a compact global attractor, or the solutions are unbounded. 相似文献
19.
《Annals of Differential Equations》2012,(2):153-156
In this paper, we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem. By the infinite dimensional Morse theory, under some conditions on nonlinear term, we obtain that there exist at least two nontrivial solutions. 相似文献
20.
Multiple solutions for fourth-order boundary value problem 总被引:4,自引:0,他引:4
In this paper, we study the existence and multiplicity of nontrivial solutions for the fourth-order two point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the fourth-order two point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions. 相似文献