Existence and Multiplicity for Elliptic Problems with Quadratic Growth in the Gradient |
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| Authors: | Louis Jeanjean Boyan Sirakov |
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| Institution: | 1. Laboratoire de Mathématiques (UMR 6623) , Université de Franche-Comté , Besan?on , France louis.jeanjean@univ-fcomte.fr;3. Departamento de Matemática , Pontifícia Universidade Católica do Rio de Janeiro , Rio de Janeiro , Brazil |
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| Abstract: | We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule. |
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| Keywords: | Elliptic equation Natural growth Non-coercive Quadratic growth in the gradient Sub- and super-solutions Variational methods |
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