Document Zbl 1027.47044

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Semilinear equations in Hilbert spaces with quasi-positive nonlinearity. (English) Zbl 1027.47044

Stud. Univ. Babeș-Bolyai, Math. 46, No. 4, 89-94 (2001).

Summary: The problem is to show that \(Ax+F(x)=0\) has a solution, where \(A\) is linear, maximal monotone, and the linearity \(F\) is a quasi-positive operator of Leray-Schauder type. The existence result is obtained as a consequence of the properties of the Leray-Schauder degree. Finally, some applications are given.

Cited in 1 Document

MSC:

47H05	Monotone operators and generalizations
47H11	Degree theory for nonlinear operators

Keywords:

quasipositive operators; Leray-Schauder degree; semilinear equation; Hilbert space

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