Generalized quasilinearization for nonlinear elliptic problems via nonvariational method (Q2783616)

This paper deals with the generalized quasilinearization method for the nonlinear elliptic BVP when the right-hand side being the sum of a convex and a concave function, that is NEWLINE\[NEWLINE\begin{cases} -\text{div }a(Du)+ C(x)u= \widetilde f(x,u)\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega,\end{cases}NEWLINE\]NEWLINE where \(\widetilde f:\overline\Omega\times \mathbb{R}\to\mathbb{R}\) is a Carathéodory function, \(a: \mathbb{R}^n\to \mathbb{R}^n\) is the given smooth vector field and \(\Omega\) is a bounded domain with smooth boundary \(C(x)\geq C_0> 0\) and \(c\in L^\infty(\Omega)\).