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 $\mu|z|^q z$, 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 $\lambda$ of the Robin condition tends to infinity. 

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