Abstract
Given a linear Sturm-Liouville operator Lu=(pu′)′ — qu and a nonlinear Nemytskij operator F(u)=f(,u,u′), we prove existence theorems for the equation Lu=F(u) by means of sharp fixed point theorems for the (usually noncompact) operator A=L−1F. By a "sharp fixed point theorem" we mean the problem of finding or estimating the highest admissible growth and non-compactness of A still guaranteeing the existence of fixed points.
Key words
- Fixed point theorems
- Nemytskij operator
- Sturm-Liouville problem
- AMS Classification
- 47H10
- 47H09
- 47H15
- 34A34
- 35J60
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Literatur
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© 1983 Springer-Verlag
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Appell, J. (1983). "Genaue" Fixpunktsätze und nichtlineare Sturm - Liouville - Probleme. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103233
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DOI: https://doi.org/10.1007/BFb0103233
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