Periodic solutions for nonlinear differential equations with maximal monotone terms
The authors study nonlinear periodic problems for scalar and vector differential inclusions involving a maximal monotone operator which is not necessarily defined everywhere. In the scalar case, they study the problem \[ (a(x(t))x'(t))'\in A(x(t))+f(t,x(t),x'(t)) \quad \text{a.e on } T=[0,b], \] \[ x(0)=x(b),\quad x'(0)=x'(b), \] and, in the vector case, the problem \[ (a(x'(t)))'\in A(x(t))+f(t,x(t),x'(t)) \quad \text{a.e on} T=[0,b], \] \[ x(0)=x(b),\quad x'(0)=x'(b). \] Their approach is based on the theory of nonlinear operators of monotone type and on the Leray-Schauder alternative principle.
scientific article; zbMATH DE number 1880010