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Nonlocal problems for parabolic inclusions. (English) Zbl 1187.35300

Summary: We investigate a class of parabolic inclusions with a nonlocal condition of integral type. We provide sufficient conditions that guarantee the existence of at least one solution. Our technique is based on Green’s function for linear parabolic partial differential equations and fixed point theorems for multivalued maps.

MSC:

35R70 PDEs with multivalued right-hand sides
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35C15 Integral representations of solutions to PDEs
35A08 Fundamental solutions to PDEs