Analysis of a nonlinear boundary value problem with p-Laplacian operator and Robin-type nonlinear boundary condition

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Résumé

In this paper, we study the existence of a solution of a nonlinear system involving the p-Laplace operator, a reaction
of the form μ|z|q z, a general nonlinearity f (z) with nonhomogeneous and nonlinear Robin-type boundary conditions. We
prove the existence and uniqueness of a weak solution to this problem by reformulating the system and applying Kakutani’s
fixed point theorem. We also examine the asymptotic behavior of the solution when the parameter λ of the Robin condition
tends to infinity.

Mots-clés

Nonlinear system, p-laplacian operator, Robin-type boundary conditions, Kakutani fixed point.