Existence of solutions of a non-linear eigenvalue problem with a variable weight |
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Authors: | Rejeb Hadiji François Vigneron |
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Institution: | Université Paris-Est, Laboratoire d''Analyse et de Mathématiques Appliquées, UMR 8050 du CNRS, 61, avenue du Général de Gaulle, F-94010, Créteil, France |
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Abstract: | We study the non-linear minimization problem on with , and : where presents a global minimum α at with . In order to describe the concentration of around , one needs to calibrate the behavior of with respect to s. The model case is In a previous paper dedicated to the same problem with , we showed that minimizers exist only in the range , which corresponds to a dominant non-linear term. On the contrary, the linear influence for prevented their existence. The goal of this present paper is to show that for , and , minimizers do exist. |
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Keywords: | 35A01 35A15 35J57 35J62 Critical Sobolev exponent Minimization problem Non-linear effects |
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