Nonlinear nonhomogeneous Dirichlet problems with singular and convection terms

Abstract

Abstract We consider a nonlinear Dirichlet problem driven by a general nonhomogeneous differential operator and with a reaction exhibiting the combined effects of a parametric singular term plus a Carathéodory perturbation f ( z , x , y ) $f(z,x,y)$ which is only locally defined in x ∈ R $x \in {\mathbb {R}} $ . Using the frozen variable method, we prove the existence of a positive smooth solution, when the parameter is small.

Keywords

• Frozen variable method
• Nonlinear regularity
• Minimal positive solution
• Leray–Schauder alternative principle
• Truncation
• Fixed point