Some results on strongly nonlinear anisotropic differential equations
Volume 37 / 2010
Applicationes Mathematicae 37 (2010), 375-386
MSC: 35J25, 35J60, 35J70.
DOI: 10.4064/am37-3-7
Abstract
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 $u.$
