On the uniqueness of the second bound state solution of a semilinear equation
Carmen Cortázar, Marta García-Huidobro, Cecilia S. Yarur (2009)
Annales de l'I.H.P. Analyse non linéaire
Tadie (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Eduardo Casas, Mariano Mateos, Jean-Pierre Raymond (2009)
ESAIM: Control, Optimisation and Calculus of Variations
We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared with some previous ones in the literature and are checked by a numerical experiment. A detailed study of the regularity of the solutions of the PDEs is carried out.
Eduardo Casas, Mariano Mateos, Jean-Pierre Raymond (2008)
ESAIM: Control, Optimisation and Calculus of Variations
We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared with some previous ones in the literature and are checked by a numerical experiment. A detailed study of the regularity of the solutions of the PDEs is carried out.
Yuan, Chunmei, Guo, Shujuan, Tong, Kaiyu (2010)
Mathematical Problems in Engineering
Shibata, Tetsutaro (2005)
Abstract and Applied Analysis
Xavier Cabré, Joana Terra (2009)
Journal of the European Mathematical Society
Alves, Claudianor O., Soares, Sérgio H.M., Souto, Marco A.S. (2011)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Anedda, Claudia, Porru, Giovanni (2011)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Tomasz Klimsiak, Andrzej Rozkosz (2016)
Colloquium Mathematicae
We are mainly concerned with equations of the form -Lu = f(x,u) + μ, where L is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, f satisfies the monotonicity condition and mild integrability conditions, and μ is a bounded smooth measure. We prove general results on existence, uniqueness and regularity of probabilistic solutions, which are expressed in terms of solutions to backward stochastic differential equations. Applications include equations with nonsymmetric...
Aleksandra Orpel (2006)
Applicationes Mathematicae
We investigate the existence of positive solutions and their continuous dependence on functional parameters for a semilinear Dirichlet problem. We discuss the case when the domain is unbounded and the nonlinearity is smooth and convex on a certain interval only.
Bernhard Ruf, P.N. Srikanth (2010)
Journal of the European Mathematical Society
We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in , and look for solutions which are invariant under a fixed point free 1-parameter group action. We show that this problem can be reduced to a nonhomogeneous equation on a related annulus in dimension 3. The ground state solutions of this equation are single peak solutions which concentrate near the inner boundary. Transforming back, these solutions produce a family of solutions which concentrate...
Matoussi, Anis, Xu, Mingyu (2008)
Electronic Journal of Probability [electronic only]
Qi-Wu Du, Chun-Lei Tang (2014)
Annales Polonici Mathematici
Some solutions are obtained for a class of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents by variational methods and some analysis techniques.
Jeanjean, Louis (2011)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Olivier Druet, Paul Laurain (2010)
Journal of the European Mathematical Society
We investigate problems connected to the stability of the well-known Pohoˇzaev obstruction. We generalize results which were obtained in the minimizing setting by Brezis and Nirenberg [2] and more recently in the radial situation by Brezis and Willem [3].
Louis Dupaigne, Alberto Farina (2010)
Journal of the European Mathematical Society
Several Liouville-type theorems are presented for stable solutions of the equation in , where is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.
Dinu, Teodora-Liliana (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Vincent Millot, Adriano Pisante (2010)
Journal of the European Mathematical Society
We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in satisfying a natural energy bound. Up to translations and rotations,such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group.
Minh-Binh Tran (2014)
Open Mathematics
In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.