共查询到20条相似文献,搜索用时 15 毫秒
1.
We study a class of superlinear elliptic problems under the Dirichlet boundary condition on a bounded smooth domain in . Assuming that the nonlinearity is superlinear in a neighborhood of , we study the dependence of the number of signed and sign-changing solutions on the parameter .
2.
Meijun Zhu 《Journal of Differential Equations》2003,193(1):180-195
In this paper we prove the existence of positive solutions to some nondivergent elliptic equations with indefinite nonlinear boundary conditions. The proof is based on a new Liouville-type theorem about the nonnegative solutions to some canonical indefinite elliptic equations, which is also proved in this paper by the method of moving planes. 相似文献
3.
Nikolaos S. Papageorgiou Eugénio M. Rocha Vasile Staicu 《Calculus of Variations and Partial Differential Equations》2008,33(2):199-230
In this paper we study second order elliptic equations driven by the Laplacian and p-Laplacian differential operators and
a nonlinearity which is (p-)superlinear (it satisfies the Ambrosetti–Rabinowitz condition). For the p-Laplacian equations
we prove the existence of five nontrivial smooth solutions, namely two positive, two negative and a nodal solution. Finally
we indicate how in the semilinear case, Morse theory can be used to produce six nontrivial solutions.
This paper was completed while the first author was visiting the University of Aveiro as an Invited Scientist. The hospitality
and financial support of the host institution are gratefully acknowledged. The second and third authors acknowledge the partial
financial support of the Portuguese Foundation for Science and Technology (FCT) under the research project POCI/MAT/55524/2004. 相似文献
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D. D. Hai 《Proceedings of the American Mathematical Society》2003,131(8):2409-2414
We establish existence and multiplicity of positive solutions to the quasilinear boundary value problem
where is a bounded domain in with smooth boundary , is continuous and p-sublinear at and is a large parameter.
where is a bounded domain in with smooth boundary , is continuous and p-sublinear at and is a large parameter.
7.
This paper concerns semilinear elliptic equations of the form – u+m(x)u=a(x)u
p
, wherea changes sign. We discuss the question of existence of positive solutions when the linear part is not coercive.This article was processed by the author using the LATEX style file pljourlm from Springer-Verlag. 相似文献
8.
We prove the existence of four solutions for the p-Laplacian equation
9.
J. López—Gómez 《偏微分方程通讯》2013,38(11-12):1787-1804
In this work we show the existence and stability of positive solutions for a general calss of semilinear elliptic boundary value problems of superlinear type with indedefinite weight functions. Optimal necessary and sufficient conditions are found. 相似文献
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Everaldo S. Medeiros Uberlandio B. Severo Elves A. B. Silva 《Calculus of Variations and Partial Differential Equations》2014,50(3-4):751-777
In this paper we apply variational and sub-supersolution methods to study the existence and multiplicity of nonnegative solutions for a class of indefinite semilinear elliptic problems that depend on a parameter. The results on the existence of solutions do not impose any growth condition at infinity on the term which depends on the parameter. To derive such results, first we find a positive supersolution by solving an auxiliary problem. Then we use a truncation argument and a global minimization method. The main hypothesis for the existence of two nonzero solutions is that the indefinite term is the product of a weight function, having a thick zero set, and a nonlinear function which satisfies the Ambrosetti–Rabinowitz superlinear condition. Results for some corresponding indefinite problems are also established. 相似文献
12.
Miguel Ramos 《Journal of Mathematical Analysis and Applications》2009,352(1):246-258
We study the existence, multiplicity and shape of positive solutions of the system −ε2Δu+V(x)u=K(x)g(v), −ε2Δv+V(x)v=H(x)f(u) in RN, as ε→0. The functions f and g are power-like nonlinearities with superlinear and subcritical growth at infinity, and V, H, K are positive and locally Hölder continuous. 相似文献
13.
Summary. In this paper we study the numerical behaviour of elliptic
problems in which a small parameter is involved and an example
concerning the computation of elastic arches is analyzed using this
mathematical framework. At first, the statements of the problem and its
Galerkin approximations are defined and an asymptotic
analysis is performed. Then we give general conditions ensuring that
a numerical scheme will converge uniformly with respect to the small
parameter. Finally we study an example in
computation of arches working in linear elasticity conditions. We build one
finite element scheme giving a locking behaviour, and another one
which does not.
Revised version received October 25, 1993 相似文献
14.
The existence of three nontrivial solutions for a class of superlinear elliptic equations is obtained by using variational theorems of mixed type due to Marino and Saccon and Linking Theorem. 相似文献
15.
Francisco Julio S.A. Corrêa 《Journal of Mathematical Analysis and Applications》2005,310(1):177-187
In this paper we study existence and uniqueness of solutions to some cases of the following nonlocal elliptic problem:
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Marco Rigoli Alberto G. Setti 《NoDEA : Nonlinear Differential Equations and Applications》2002,9(1):15-36
We give sufficient conditions for non-existence of positive solutions of the equation on a cone of We further analyze the existence of positive solutions in the radial, subcritical case, and show that under suitable conditions
on the coefficients, every radial solution whose value in 0 is sufficiently large must vanish.
Received April 2000 相似文献
18.
We study the existence of multiple positive solutions for a superlinear elliptic PDE with a sign-changing weight. Our approach is variational and relies on classical critical point theory on smooth manifolds. A special care is paid to the localization of minimax critical points. 相似文献
19.
Marius Ghergu 《Journal of Mathematical Analysis and Applications》2005,311(2):635-646
We establish several results related to existence, nonexistence or bifurcation of positive solutions for the boundary value problem −Δu+K(x)g(u)+a|∇u|=λf(x,u) in Ω, u=0 on ∂Ω, where Ω⊂RN(N?2) is a smooth bounded domain, 0<a?2, λ is a positive parameter, and f is smooth and has a sublinear growth. The main feature of this paper consists in the presence of the singular nonlinearity g combined with the convection term a|∇u|. Our approach takes into account both the sign of the potential K and the decay rate around the origin of the singular nonlinearity g. The proofs are based on various techniques related to the maximum principle for elliptic equations. 相似文献
20.
Adimurthi Jacques Giacomoni 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(1):1-20
This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
We consider a function h which is smooth and changes sign. 相似文献