On the normalized eigenvalue problems for nonlinear elliptic operators. II (Q2642101)

Let \(X\) be a real reflexive Banach space such that both \(X\) and \(X^*\) are locally uniformly convex spaces. This paper deals with the nonlinear eigenvalue problem \(Au=C(\lambda ,u)\), \(u\geq 0\) and \(u\in\partial D\), where \(A:X\rightarrow X\) is a maximal monotone operator, \(D\) is a bounded open subset of \(X\), and \(C\) is a nonlinear operator defined on \(\mathbb R_+\times\partial D\). The paper is devoted to the qualitative analysis of nonlinear eigenvalue problems of this type, including the case where \(A\) is a bounded and demicontinuous \((S)_+\) operator. Applications to nonlinear elliptic equations under degenerate and singular conditions are also provided. [Part I has appeared ibid. 329, No. 1, 51--64 (2007; Zbl 1112.47051).]