Some eigenvalue results for perturbations of maximal monotone operators (Q395773)

Let \(X\) be a reflexive Banach space, \(X^\ast\) its dual and \(\Omega\) be an open bounded subset in \(X\). Assume that \(T: D(T)\subset X\to X^\ast\) is a maximal monotone operator and \(C: (0,\infty)\times\overline{\Omega} \to X^\ast\) is a bounded demicontinuous operator satisfying property \((S)\). In this paper, the implicit eigenvalue problem \(Tx+C(\lambda,x)=0\) is solved by using the Browder degree. The problem \(Tx+\lambda Cx=0\), where \(C\) is a generalized pseudomonotone, quasi-bounded densely defined operator is solved by using the Kartsatos-Skrypnik degree for some densely defined perturbations of maximal monotone operators.