Quasilinear differential equations depending on a maximal monotone operator (Q5929083)

The author proves the existence of solutions to the nonlinear boundary value problem NEWLINE\[NEWLINE-(\|x'(t)\|^{p- 2} x'(t))'+ Ax(t)\ni f(t,x(t), x'(t)),\quad\text{a.e. on }T= [0,b],\quad x(0)= x(b)= 0,NEWLINE\]NEWLINE where \(p\geq 2\), \(A: \mathbb{R}^N\to \mathbb{R}^N\) is a maximal monotone (possibly multivalued) operator, and \(f: T\times \mathbb{R}^N\times \mathbb{R}^N\to \mathbb{R}^N\) is a Carathéodory function. The approach relies on monotonicity and Leray-Schauder-type arguments.