Anti-periodic solutions for second order differential inclusions

Abstract

In this paper, we extend the existence results presented in [9] for $L^{p}$ spaces to operator inclusions of Hammerstein type in $W^{1,p}$ spaces. We also show an application of our results to anti-periodic boundary-value problems of second-order differential equations with nonlinearities depending on $u'$.

Keywords

• Anti-periodic solution
• nonlinear boundary-value problem
• dissipative operator
• multivalued mapping
• fixed point.