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Existence theorems for a multivalued boundary value problem. (English) Zbl 0741.34008
The multivalued boundary value problem $$u''\in F(t,u,u')$$, $$u(a)=u(b)=0$$, is considered where $$F$$ has closed convex values in $$R^ n$$, the graphs of $$F(t,\centerdot,\centerdot)$$ are closed, the maps $$F(\centerdot,u,u')$$ are measurable and $$F$$ is bounded in some sense. The existence of solutions $$u\in W^{2,p}([a,b],R^ n)$$ is proved using a recent existence result for operator inclusions.

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 34A60 Ordinary differential inclusions 47J25 Iterative procedures involving nonlinear operators 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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##### References:
 [1] Erbe, Lecture Notes in Pure and Appl. Math. 127 pp 115– (1991) [2] Cinquini, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2) 8 pp 1– (1939) [3] Bernfeld, An introduction to nonlinear boundary value problems (1974) · Zbl 0286.34018 [4] Dragoni, Rend. Sem. Mat. Univ. Roma (4) 2 pp 255– (1938) [5] Frigon, C.R. Acad. Sci. Paris. Série I Math. 310 pp 819– (1990) [6] Pruszko, Dissertationes Math. 229 pp 1– (1984) [7] DOI: 10.1080/00036819008839966 · Zbl 0687.47044 [8] Hartman, Ordinary differential equations (1964) · Zbl 0125.32102 [9] Granas, C.R. Acad. Sci. Paris. Série I Math. 307 pp 391– (1988) [10] DOI: 10.1007/BF02844525 · Zbl 0698.34019
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