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.
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Literatur
Darbo, G.: Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24, 84–92 (1955)
Sadovskij, B. N.: Nichtkompaktheitsmasse und kondensierende Operatoren (Russisch), Probl. Mat. Anal. Slozhn. Sistem, Voronezh, 89–119 (1968)
Dunford, N. / Schwartz, J.: Linear operators II, Int. Publ. 1963
Appell, J. / Zabrejko, P. P.: On a theorem of M. A. Krasnosel'skij, erscheint in Nonlin. Anal. TMA
Appell, J.: On the solvability of nonlinear noncompact problems in function spaces with applications to integral and differential equations, erscheint in Boll. Unione Mat. Ital.
Krasnosel'skij, M. A. / Rutitskij, Ja. B.: Convex functions and Orlicz spaces, Noordhoff Groningen 1961
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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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