Note on spectral theory of nonlinear operators: Extensions of some surjectivity theorems of Fučík and Nečas. (English) Zbl 0546.47029

Pacella, Filomena

Czech. Math. J. 34(109), 28-45 (1984).

In this paper the existence of solutions of the equation: \[ \lambda T(x)-S(x)=f,\quad x\in X,\quad f\in Y,\quad\lambda \in R \] is studied, under the assumptions that X and Y are reflexive Banach spaces, the dual space Y’ is strictly convex, S is a bounded weakly closed operator and T is a bijective operator between X and Y. The results obtained here extend some theorems of Fučik and Nečas where S is supposed completely continuous. The method used is a topological degree theory for noncompact operators.

MSC:

47J10	Nonlinear spectral theory, nonlinear eigenvalue problems
47J05	Equations involving nonlinear operators (general)
35P05	General topics in linear spectral theory for PDEs

Keywords:

nonlinear spectral theory; surjectivity theorems; quasilinear elliptic equations; strictly convex; bounded weakly closed operator; topological degree theory for noncompact operators

References:

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