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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
2.
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Proceedings of the American Mathematical Society》2004,132(2):429-434
In this paper we study a nonlinear periodic problem driven by the ordinary scalar p-Laplacian and with a Carathéodory nonlinearity. We establish the existence of at least two nontrivial solutions. Our approach is variational based on the smooth critical point theory and using the ``Second Deformation Theorem".
3.
Shaowei Chen 《Journal of Mathematical Analysis and Applications》2008,343(2):681-705
In this paper, we consider a simplified two fluid system in plasma theory. Some multiple existence results for this system are obtained by variational methods and topological degree methods. 相似文献
4.
Zhaoxia Liu 《Journal of Mathematical Analysis and Applications》2011,382(2):731-747
In this paper, we consider the elliptic system of two equations in H1(RN)×H1(RN):
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Petru Jebelean Gheorghe Moro?anu 《Journal of Mathematical Analysis and Applications》2006,313(2):738-753
This paper is concerned with the existence of solutions for the boundary value problem
7.
In this paper, the fuzzy Basset equation is introduced. This problem is related to the motion of a sphere in a viscous liquid when its parameters are fuzzy numbers. We investigate the existence and uniqueness of solution with converting the problem to a system of fuzzy fractional differential equation, and the solution is also obtained under Caputo generalized Hukuhara differentiability. Some examples show the effectiveness and efficiency our approach. 相似文献
8.
In this paper, we use new analyses to assert that there are three positive solutions of Eq. (1.1) in infinite cylinder domain with hole . 相似文献
9.
Antonella Fiacca Nikolaos Matzakos Nikolaos S. Papageorgiou Raffaella Servadei 《Proceedings Mathematical Sciences》2001,111(4):489-508
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities.
First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is
defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between
them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed
by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This
case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that
the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity.
Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial
solutions (multiplicity theorem). 相似文献
10.
Kuan-Ju Chen 《Journal of Mathematical Analysis and Applications》2006,319(2):841-862
In this paper, we study the existence of positive solutions of some nonlinear elliptic problems in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. 相似文献