Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 2, pp. 287 - 295 (1999)
Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales
J. JannoJ. Janno: Estonian Academy of Sciences, Institute of Cybernetics, Akadeemia teer 21, EE-0026 Tallinn, Estonia.
Abstract: By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations $u + G_0[D,u] + L(G_1[D,u],G_2[D,u]) = f$ 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.
Keywords: nonlinear operator equations, nonlinear convolution equations, scales of norms, fixed point theorems, existence, uniqueness and stability of solutions of nonlinear equations
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