NONLINEAR VARIATIONAL EVOLUTION INEQUALITIES WITH NONLOCAL CONDITIONS
Copyright policy )NONLINEAR VARIATIONAL EVOLUTION INEQUALITIES WITH NONLOCAL CONDITIONS
The authors prove existence, uniqueness and regularity results for the following nonlinear functional differential problem with nonlocal initial condition: \[ \frac{d}{dt} x(t)+Ax(t)+ \partial\Phi\bigl(x(t)\bigr)\ni f \bigl(t,x(t)+k(t),\bigr),\quad 00\), \(k\in L^2(0,T:H)\) and \(x_0\in\overline{D(\Phi)}\). To illustrate the applicability of this work an example is given in Section 4.
nonlinear functional differential problem, Partial functional-differential equations, Initial value problems for nonlinear first-order PDEs, Nonlinear parabolic equations, Periodic solutions to ordinary differential equations, Variational inequalities, nonlocal initial condition
nonlinear functional differential problem, Partial functional-differential equations, Initial value problems for nonlinear first-order PDEs, Nonlinear parabolic equations, Periodic solutions to ordinary differential equations, Variational inequalities, nonlocal initial condition
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