A topological and geometric approach to fixed points results for sum of operators and applications. (English) Zbl 1078.47014
The authors prove a fixed point result of Krasnoselskii type for the sum \(A+B\), where \(A\) and \(B\) are continuous maps acting on locally convex spaces. In many applications, the original hypotheses of Krasnoselskii are difficult to meet and quite restrictive. The authors construct their hypotheses after a rigorous confrontation with this fact and the previous literature on the subject.
All the generality of the results is used in the subsequent applications, that are “per se” interesting: an elliptic equation with lack of compactness and a nonlinear integral equation.
All the generality of the results is used in the subsequent applications, that are “per se” interesting: an elliptic equation with lack of compactness and a nonlinear integral equation.
Reviewer: Espedito De Pascale (Rende)
MSC:
| 47H10 | Fixed-point theorems |
| 47N20 | Applications of operator theory to differential and integral equations |
| 45G10 | Other nonlinear integral equations |
| 35J60 | Nonlinear elliptic equations |
| 47H30 | Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) |
Keywords:
fixed point results of Krasnoselsky type; locally convex topological spaces; nonlinear integral equations; elliptic equations with critical exponentsReferences:
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