Nonlinear nonhomogeneous Robin problems with dependence on the gradient

Abstract

Abstract We consider a nonlinear elliptic equation driven by a nonhomogeneous partial differential operator with Robin boundary condition and a convection term. Using a topological approach based on the Leray–Schauder alternative principle, together with truncation and comparison techniques, we show the existence of a smooth positive solution without imposing any global growth condition on the reaction term.

Keywords

• Nonhomogeneous differential operator
• Robin boundary condition
• Nonlinear regularity theory
• Convection term
• Leray–Schauder alternative theorem
• Positive solution