Existence and multiplicity for elliptic problems with quadratic growth in the gradient

Details Existence and multiplicity for elliptic problems with quadratic growth in the gradient Existence and multiplicity for elliptic problems with quadratic growth in the gradient

2010-10-21

arxiv.org/abs/1010.4520v1

Mathematics

Analysis of PDEs

Scientific paper

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable. 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. Our proofs are mainly variational but sub- and super-solutions arguments are also used.

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