Nonlinear multivalued boundary value problems (Q2746647)

The authors prove existence theorems for the following problem: NEWLINE\[NEWLINE(\|x'(t)\|^{p-2}x'(t))'\in A(x(t)) + F(t,x(t),x'(t)), \quad \text{a.e. on } T =[0,b],NEWLINE\]NEWLINE NEWLINE\[NEWLINE(\varphi(x'(0))-\varphi(x'(b))) \in\xi(x(0),x(b)),\quad 2\leq p<\infty.NEWLINE\]NEWLINE Here, \(A:\mathbb{R}^{N}\to 2^{\mathbb{R}^{N}}\) is a maximal monotone map, \(F:T\times \mathbb{R}^{N}\times \mathbb{R}^{N}\to 2^{\mathbb{R}^{N}}\) is a multifunction and \(\varphi:\mathbb{R}^{N}\to \mathbb{R}^{N}\) is defined by \(\varphi(r)=\|r\|^{p-2}r,\) \(\xi: \mathbb{R}^{N}\times \mathbb{R}^{N}\to 2^{\mathbb{R}^{N}\times \mathbb{R}^{N}}.\)