Xing Zhang, Xia Zhang, Yongqiang Fu (2010)
Annales Polonici Mathematici
Similarity:
We study the multiplicity of solutions for a class of p(x)-Laplacian equations involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going toward infinity.
Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani (2014)
Applicationes Mathematicae
Similarity:
We study the existence of solutions for a p-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.
Mohsen Khaleghi Moghadam, Johnny Henderson (2017)
Open Mathematics
Similarity:
Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.
J. Chabrowski, Jianfu Yang (2001)
Colloquium Mathematicae
Similarity:
We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.
Damian Wiśniewski, Mariusz Bodzioch (2016)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Similarity:
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
E.B. Davies (1984/85)
Mathematische Zeitschrift
Similarity:
A. Benedek, R. Panzone (1990)
Colloquium Mathematicae
Similarity:
J. Chabrowski, P. Drábek (2002)
Studia Mathematica
Similarity:
We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.
Bruno Nazaret (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This article is devoted to the study of a perturbation with a viscosity term in an elliptic equation involving the -Laplacian operator and related to the best contant problem in Sobolev inequalities in the critical case. We prove first that this problem, together with the equation, is stable under this perturbation, assuming some conditions on the datas. In the next section, we show that the zero solution is strongly isolated in some sense, among the space of the solutions. Actually,...
Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)
Banach Center Publications
Similarity:
In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.
Xia Zhang, Yongqiang Fu (2009)
Annales Polonici Mathematici
Similarity:
We study a class of hemivariational inequalities with p(x)-Laplacian. Applying nonsmooth critical point theory for locally Lipschitz functions, we obtain the existence of solutions on interior and exterior domains.
J. Chabrowski, Jianfu Yang (2003)
Rendiconti del Seminario Matematico della Università di Padova
Similarity:
Jan Chabrowski (2004)
Colloquium Mathematicae
Similarity:
We consider the Neumann problem involving the critical Sobolev exponent and a nonhomogeneous boundary condition. We establish the existence of two solutions. We use the method of sub- and supersolutions, a local minimization and the mountain-pass principle.
Katarzyna Pietruska-Pałuba, Andrzej Stós (2013)
Studia Mathematica
Similarity:
Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.
Nikolaos Kourogenis, Nikolaos Papageorgiou (1998)
Colloquium Mathematicae
Similarity:
In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.
Nikolaos Papageorgiou, Francesca Papalini (2000)
Annales Polonici Mathematici
Similarity:
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
Samira Benmouloud-Sbai, Mohamed Guedda (2003)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Similarity:
Marcello Lucia, Paola Magrone, Huan-Song Zhou (2003)
Revista Matemática Complutense
Similarity:
This paper deals with the problem of finding positive solutions to the equation -∆[u] = g(x,u) on a bounded domain 'Omega' with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour. The solutions are found using the Mountain Pass Theorem.