On perturbations of accretive operators in Banach spaces
Let \(X\) be a Banach space, \(A:D(A)\subset X \to 2^X\) be an \(m\)-accretive mapping and \(\Omega\subset X\) be an open bounded subset with \(\overline{\Omega}\cap D(A)\not=\emptyset\). Let \(p\in X\) and \(C:D(A)\cap\overline{\Omega}\to X\) satisfy the condition that \((I-\lambda C)(I+\lambda A)^{-1}:X\to X\) is a continuous condensing mapping for some \(\lambda>0\) and \(C(D(A)\cap \overline{\Omega}\) is bounded. By using the topological degree of condensing mappings, the author proved that \(p\in (A+C)(D(A)\cap\overline{\Omega})\) if there exists \(z\in D(A)\cap\Omega\) such that \(\langle u+Cx-p,j\rangle\geq 0\) for all \(x\in D(A)\cap \partial\Omega\), \(u\in Ax\), and \(j\in J(x-z)\), where \(J\) is the normal duality mapping. The author extended this result in several directions and gave some applications.
scientific article; zbMATH DE number 1626232