On the solvability in Hilbert space of certain nonlinear operator equations depending on parameters
Let H be a real separable Hilbert space, D be a closed ball in H, \(A: D\to H\) and \(C: D\to H\) be monotone and compact (i.e. completely continuous) operators, respectively. Let \(T: H\to H\) be a linear, compact, self-adjoint and positive-definite operator. Using the degree theory of \textit{F. E. Browder} [Proc. Sympos. Pure Math. 18, Part II (1976; Zbl 0327.47022)], the authors in three theorems prove that, under additional assumptions, the equation \(Au-\lambda Tu+\mu Cu=f\) is solvable, where \(\lambda,\mu >0\) are fixed constants and \(f\in H\). In particular, Theorem 3 improves a result of \textit{S. Kesavan} [Appl. Anal. 16, 279-290 (1983; Zbl 0515.35031)].
scientific article; zbMATH DE number 4007073