Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales

Jaan Janno

doi:10.4171/zaa/882

JournalszaaVol. 18, No. 2pp. 287–295

Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales

Jaan Janno
Tallin Technical University, Estonia

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Abstract

By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations $u + G_{0} [D, t L] + L (G_{1} [D, u], G 2 [D, u]) = f$ in a Banach space $E$ , where $G_{0}, G_{1}, G_{2}$ 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.

Cite this article

Jaan Janno, Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales. Z. Anal. Anwend. 18 (1999), no. 2, pp. 287–295

DOI 10.4171/ZAA/882