共查询到11条相似文献,搜索用时 0 毫秒
1.
Leszek Gasiński 《Mathematische Nachrichten》2008,281(12):1728-1746
In this paper we consider quasilinear hemivariational inequality at resonance. We prove existence results for strongly resonant quasilinear problem, resonant problem under a Tang‐type condition as well as two multiplicity results. The method of the proofs is based on the nonsmooth critical point theory for locally Lipschitz functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Leszek Gasiński 《Journal of Mathematical Analysis and Applications》2002,276(2):723-746
In this paper we study a hyperbolic hemivariational inequality with a nonlinear, pseudomonotone operator depending on the derivative of an unknown function and a linear, monotone operator depending on an unknown function. Using the surjectivity result for L-pseudomonotone operators, an existence result for such inequalities is proved. 相似文献
3.
Sophia Th. KyritsiNikolaos S. Papageorgiou 《Journal of Mathematical Analysis and Applications》2002,276(1):292-313
In this paper we examine an obstacle problem for a nonlinear hemivariational inequality at resonance driven by the p-Laplacian. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functionals defined on a closed, convex set, we prove two existence theorems. In the second theorem we have a pointwise interpretation of the obstacle problem, assuming in addition that the obstacle is also a kind of lower solution for the nonlinear elliptic differential inclusion. 相似文献
4.
Leszek Gasiński Dumitru Motreanu Nikolaos S. Papageorgiou 《Proceedings Mathematical Sciences》2006,116(2):233-255
We consider a semilinear elliptic equation with a nonsmooth, locally Lipschitz potential function (hemivariational inequality).
Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our approach is based
on the nonsmooth critical point theory for locally Lipschitz functionals and uses an abstract multiplicity result under local
linking and an extension of the Castro-Lazer-Thews reduction method to a nonsmooth setting, which we develop here using tools
from nonsmooth analysis. 相似文献
5.
A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained. 相似文献
6.
We study nonautonomonus second order periodic systems with a nonslnooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity. 相似文献
7.
Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems 总被引:1,自引:0,他引:1
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Czechoslovak Mathematical Journal》2004,54(2):347-371
In this paper we examine nonlinear periodic systems driven by the vectorial p-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the sublinear problem. For the semilinear problem (i.e. p = 2) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the superlinear problem. Our work generalizes some recent results of Tang (PAMS 126(1998)). 相似文献
8.
We study nonlinear elliptic problems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential (hemivariational inequality). We do not assume that the nonsmooth potential satisfies the Ambrosetti--Rabinowitz condition. Using a variational approach based on the nonsmooth critical point theory, we establish the existence of at least one smooth positive solution.Mathematics Subject Classifications (2000). 35J50, 35J85, 35R70.This article is Revised version.Leszek Gasiski is an award holder of the NATO Science FellowshipProgramme, which was spent in the National Technical University of Athens. 相似文献
9.
In this paper we examine a nonlinear elliptic problem driven by the p-Laplacian differential operator and with a potential function which is only locally Lipschitz, not necessarily C1 (hemivariational inequality). Using the nonsmooth critical point theory of Chang, we obtain two strictly positive solutions.
One solution is obtained by minimization of a suitable modification of the energy functional. The second solution is obtained
by generalizing a result of Brezis-Nirenberg about the local C10-minimizers versus the local H10-minimizers of a C1-functional.
Mathematics Subject Classification (2000) 35J50, 35J85, 35R70 相似文献
10.
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Proceedings Mathematical Sciences》2004,114(3):269-298
In this paper we study second order non-linear periodic systems driven by the ordinary vectorp-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth
critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function.
Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result
(even for smooth problems) for systems monitored by thep-Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a
generalized Landesman-Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear
case the problem is at resonance at any eigenvalue. 相似文献
11.
Dimitrios Kandilakis Nikolaos C. Kourogenis Nikolaos S. Papageorgiou 《Journal of Global Optimization》2006,34(2):219-244
In this paper, we extend to nonsmooth locally Lipschitz functionals the multiplicity result of Brezis–Nirenberg (Communication
Pure Applied Mathematics and 44 (1991)) based on a local linking condition. Our approach is based on the nonsmooth critical
point theory for locally Lipschitz functions which uses the Clarke subdifferential. We present two applications. This first
concerns periodic systems driven by the ordinary vector p-Laplacian. The second concerns elliptic equations at resonance driven by the partial p-Laplacian with Dirichlet boundary condition. In both cases the potential function is nonsmooth, locally Lipschitz. 相似文献