Dirichlet problems with unbalanced growth and convection

Abstract

We consider a double phase Dirichlet problem with a gradient dependent reaction term (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a bounded strictly positive solution. Moreover, we show that the set of these solutions is compact in the corresponding generalized Sobolev–Orlicz space.

Keywords

• weighted $p$-laplacian
• eigenvalue
• generalized orlicz space
• pseudomonotone operator
• double phase