Nonlinear equations with operators satisfying generalized Lipschitz conditions in scales (Q1301250)

Summary: 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.