Abstract
We apply variational methods in order to prove that the nonlinear system (1) admits at least one regular solution.
Highlights
We apply variational methods in arder to prove that the nonlinear system {1) admits at least one regular solution
Brezis-Coron and Struwe have shown by variational methods t hat if the boundary data is small and non constant, there are at least two weak solutions
The goal of this work is to show that for non constant H, the problem may be solved by variational methods, under rather general conditions on H and the boundary data
Summary
We apply variational methods in arder to prove that the nonlinear system {1) admits at least one regular solution. { u=') in ao where H is a given continuously differentiable function and O is an open e subset of R 2 with 1 boundary. Brezis-Coron and Struwe have shown by variational methods (see [BC], [S]) t hat if the boundary data is small and non constant, there are at least two weak solutions.
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