Semilinear systems with a multi-valued nonlinear term

• Autorzy: In-Sook Kim , Suk-Joon Hong
• Języki publikacji: EN

Abstrakty

EN

Introducing a topological degree theory, we first establish some existence results for the inclusion h ∈ Lu − Nu in the nonresonance and resonance cases, where L is a closed densely defined linear operator on a Hilbert space with a compact resolvent and N is a nonlinear multi-valued operator of monotone type. Using the nonresonance result, we next show that abstract semilinear system has a solution under certain conditions on N = (N1, N2), provided that L = (L1, L2) satisfies dim Ker L1 = ∞ and dim Ker L2 < ∞. As an application, periodic Dirichlet problems for the system involving the wave operator and a discontinuous nonlinear term are discussed.

Słowa kluczowe

EN

Semilinear system; Multi-valued operator; Operators of monotone type; Degree theory

Kategorie tematyczne

• 35A16: Topological and monotonicity methods
• 35L71: Semilinear second-order hyperbolic equations
• 35B10: Periodic solutions
• 47H05: Monotone operators and generalizations
• 47H04: Set-valued operators
• 47H11: Degree theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 628-644

Daty

wydano

2017-01-01

otrzymano

2016-12-19

zaakceptowano

2017-03-21

online

2017-05-20

Twórcy

autor

In-Sook Kim

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autor

Suk-Joon Hong

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Identyfikatory

DOI

10.1515/math-2017-0056