Existence and stability of solutions of general semilinear elliptic equations with measure data

Abstract

We study existence and stability for solutions of $Lu+g(x;u)=\omega$ in the closure of open set $\Omega$ where L is a second order elliptic operator, $g$ a Caratheodory function and $\omega$ a measure in $\bar{\Omega }$. We present a uni ed theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.

arXiv commentto appear in Advanced Nonlinear Studies

Cited by in corpus (4)

• Elliptic equations involving general subcritical source nonlinearity and measures
• Semilinear fractional elliptic equations involving measures
• Schr{ö}dinger operators with Leray-Hardy potential singular on the boundary
• Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data