Multiple boundary peak solutions for some singularly perturbed Neumann problems
Changfeng Gui, Juncheng Wei, Matthias Winter (2000)
Annales de l'I.H.P. Analyse non linéaire
Kokilashvili, V., Paatashvili, V. (1997)
Memoirs on Differential Equations and Mathematical Physics
Alexander Ženíšek (1981)
Aplikace matematiky
Approximation of nonhomogeneous boundary conditions of Dirichlet and Neumann types is suggested in solving boundary value problems of elliptic equations by the finite element method. Curved triangular elements are considered. In the first part of the paper the convergence of the finite element method is analyzed in the case of nonhomogeneous Dirichlet problem for elliptic equations of order , in the second part of the paper in the case of nonhomogeneous mixed boundary value problem for second order...
Shapour Heidarkhani (2012)
Annales Polonici Mathematici
Using a recent critical point theorem due to Bonanno, the existence of a non-trivial solution for a class of systems of n fourth-order partial differential equations with Navier boundary conditions is established.
Volpert, A., Volpert, V. (2005)
Abstract and Applied Analysis
Jiří Hřebíček (1982)
Aplikace matematiky
The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit -elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform -ellipticity are found.
Candela, Anna Maria, Squassina, Marco (2003)
Serdica Mathematical Journal
2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30By means of a suitable nonsmooth critical point theory for lower semicontinuous functionals we prove the existence of infinitely many solutions for a class of quasilinear Dirichlet problems with symmetric non-linearities having a one-sided growth condition of exponential type.The research of the authors was partially supported by the MIUR project “Variational and topological methods in the study of nonlinear phenomena” (COFIN 2001)....
H. Marcinkowska (1983)
Annales Polonici Mathematici
Goncalves, J.V., Meira, S. (1998)
International Journal of Mathematics and Mathematical Sciences
Ramos, M., Rodrigues, P. (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Jean Dolbeault, Régis Monneau (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in . We prove that if the level lines of a solution have bounded curvature, then these level lines are straight lines. As a consequence, the solution is one-dimensional. The method also provides a result on free boundary problems of Serrin type.
Juncheng Wei, Liqun Zhang (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Ben Othman, Sonia (2006)
Abstract and Applied Analysis
Martin Costabel, Ernst Stephan, Wolfgang L. Wendland (1983)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Ivan Hlaváček, Michal Křížek (2001)
Applications of Mathematics
We prove that the finite element method for one-dimensional problems yields no discretization error at nodal points provided the shape functions are appropriately chosen. Then we consider a biharmonic problem with mixed boundary conditions and the weak solution . We show that the Galerkin approximation of based on the so-called biharmonic finite elements is independent of the values of in the interior of any subelement.
J. A. Nitsche (1981)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Miroslav Krbec (1976)
Commentationes Mathematicae Universitatis Carolinae
Vesa Mustonen, Matti Tienari (1999)
Mathematica Bohemica
We study the mappings of monotone type in Orlicz-Sobolev spaces. We introduce a new class as a generalization of and extend the definition of quasimonotone map. We also prove existence results for equations involving monotone-like mappings.
Rolf Rannacher (1979)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Henri Berestycki, Juncheng Wei (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
We consider the following singularly perturbed elliptic problemwhere satisfies some growth conditions, , and () is a smooth and bounded domain. The cases (Neumann problem) and (Dirichlet problem) have been studied by many authors in recent years. We show that, there exists a generic constant such that, as , the least energy solution has a spike near the boundary if , and has an interior spike near the innermost part of the domain if . Central to our study is the corresponding problem...