JournalszaaVol. 18, No. 2pp. 287–295

Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales

  • Jaan Janno

    Tallin Technical University, Estonia
Nonlinear Equations with Operators Satisfying Generalized Lipschitz Conditions in Scales cover
Download PDF

Abstract

By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations u+G0[D,tL]+L(G1[D,u],G2[D,u])=fu + G_0[D, tL] + L(G_1 [D, u], G2[D, u]) = f in a Banach space EE, where G0,G1,G2G_0, G_1 , G_2 satisfy Lipschitz conditions in scales of norms, LL is a bilinear operator and DD 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