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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 2, 1999, pp. 287–295
DOI: 10.4171/ZAA/882

Published online: 1999-06-30

Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales

Jaan Janno[1]

(1) Tallin Technical University, Estonia

By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations $u + G_0[D, tL] + L(G_1 [D, u], G2[D, u]) = f$ 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.

Keywords: Nonlinear operator equations, nonlinear convolution equations, scales of norms, fixed point theorems, existence, uniqueness and stability of solutions of nonlinear equations

Janno Jaan: Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales. Z. Anal. Anwend. 18 (1999), 287-295. doi: 10.4171/ZAA/882