An approximation approach for solving degenerated quasilinear problems

Abstract

<p style='text-indent:20px;'>The present paper develops an approximation approach for solving a quasilinear Dirichlet boundary value problem that exhibits a degenerated <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian and full dependence on the solution and its gradient (convection term). The results establish that the solution set is nonempty and bounded. The principal part of the equation is driven by a <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian type operator containing a weight depending on the solution without any monotonicity assumption. The existence of a weak solution results through a limit process by means of approximate solutions arising from finite-dimensional problems. The a priori estimates are obtained in adequate Sobolev spaces with weights. An example provides an explicit illustration of the involved technique.</p>