Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales | Zendy

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Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales

Author(s) -

Jaan Janno

Publication year - 1999

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/882

Subject(s) - lipschitz continuity , nonlinear system , mathematics , lipschitz domain , mathematical analysis , physics , quantum mechanics

By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations u + G0 [D, tL] + L(G 1 [D, u], G 2 [D, uJ) = f in a Banach space E, where Go, C 1 , C2 satisfy Lipschitz conditions in scales of norms, L is a bilinear operator and D is a data parameter. The theory is applicable for inverse problems of memory identification and generalized convolution equations of the second kind.

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