# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Some results on strongly nonlinear anisotropic differential equations

### Tom 37 / 2010

Applicationes Mathematicae 37 (2010), 375-386 MSC: 35J25, 35J60, 35J70. DOI: 10.4064/am37-3-7

#### Streszczenie

The paper concerns the existence of weak solutions to nonlinear elliptic equations of the form $A(u) + g(x, u, \nabla u) = f,$ where $A$ is an operator from an appropriate anisotropic function space to its dual and the right hand side term is in $L^{1+m}$ with $0< m< 1$. We assume a sign condition on the nonlinear term $g$, but no growth restrictions on $u.$

#### Autorzy

Faculty of Sciences
Al-Imam University
P.O. Box 90950
e-mail
• A. El KhalilDepartment of Mathematics
Faculty of Sciences
Al-Imam University
P.O. Box 90950
e-mail
• S. El ManouniDepartment of Mathematics
Faculty of Sciences
Al-Imam University
P.O. Box 90950