Nonlinear boundary value problems for second order differential inclusions
Finite-dimensional second order semilinear differential inclusions with nonlinearities being non-necessarily convex valued and satisfying weak growth of Hartman-Wintner conditions subject to nonlinear two-point boundary conditions involving maximal monotone operators are studied. Techniques from convex analysis, the so-called decomposable analysis (i.e., set-valued maps with decomposable values in the sense of Fryszkowski), theory of monotone operators together with fixed point results are employed in order to establish the existence od solutions. The general boundary conditions generalize the usual Sturm-Dirichlet boundary value problems for second order ODE.
upper semicontinuous and lower semicontinuous set-valued map
scientific article; zbMATH DE number 5539220
scientific article