Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1999-06-30
Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in ScalesJaan Janno (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