Nonlinear elliptic boundary value problems at resonance with nonlinear Wentzell boundary conditions

Details Nonlinear elliptic boundary value problems at resonance with nonlinear Wentzell boundary conditions Nonlinear elliptic boundary value problems at resonance with nonlinear Wentzell boundary conditions

2011-05-19

arxiv.org/abs/1105.3870v1

Mathematics

Dynamical Systems

Scientific paper

In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the second part, we give some additional results on existence, uniqueness and continuous dependence estimates of the weak solutions for these classes of nonlinear problems. Finally, we show that these solutions are also bounded and provide explicit estimates.

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