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

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
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### References:

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