Abstract
In this work, we prove an existence theorem of renormalized solutions for nonlinear elliptic problem of the type $$\begin{aligned} -{\text {div}}\>a(x,u,\nabla u)-\mathop {{\mathrm{div}}}\Phi (x,u)= f \quad \text {in }{\Omega }, \end{aligned}$$where the lower order term $$\Phi $$ verifies the natural growth condition $$\begin{aligned} |\Phi (x,s)|\le \gamma (x)+\overline{M}^{-1}(M(|s|)), \text { with } \gamma \in E_{\overline{M}}(\Omega ). \end{aligned}$$No $$\Delta _{2}$$-condition is needed neither on the N-function M nor on its complementary $$\overline{M}$$.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Rendiconti del Circolo Matematico di Palermo Series 2
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.