An Elliptic Problem with a Lower Order Term Having Singular Behaviour
Daniela Giachetti, François Murat (2009)
Bollettino dell'Unione Matematica Italiana
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We prove the existence of distributional solutions to an elliptic problem with a lower order term which depends on the solution in a singular way and on its gradient with quadratic growth. The prototype of the problem under consideration is where , ; , (and so ). If , we prove the existence of a solution for both the "+" and the "-" signs, while if , we prove the existence of a solution for the "+" sign only.