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On four-point boundary value problem without growth conditions. (English) Zbl 0955.34008
Summary: The author proves the existence of solutions to four-point boundary value problems under the assumption that \(f\) fulfils various combinations of sign conditions and no growth restrictions are imposed on \(f\). In contrast to earlier works all these results are proved for the Carathéodory case.

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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[1] P. Kelevedjiev: Existence of solutions for two-point boundary value problems. Nonlin. Anal. TMA 22 (1994), 217-224. · Zbl 0797.34019
[2] I. Rachůnková: A four-point problem for differential equations of the second order. Arch. Math. (Brno) 25 (1989), 175-184. · Zbl 0715.34033
[3] I. Rachůnková: Existence and uniqueness of solutions of four-point boundary value problems for 2nd order differential equations. Czechoslovak Math. Journal 39 (114) (1989), 692-700. · Zbl 0695.34016
[4] I. Rachůnková: On a certain four-point problem. Radovi Matem. 8, 1 (1992). · Zbl 0756.34026
[5] I. Rachůnková: An existence theorem of the Leray-Schauder type for four-point boundary value problems. Acta UP Olomucensis, Fac. rer. nat. 100, Math. 30 (1991), 49-59. · Zbl 0752.34016
[6] I. Rachůnková and S. Staněk: Topological degree methods in functional boundary value problems. Nonlin. Anal. TMA 27 (1996), 153-166. · Zbl 0856.34075
[7] I. Rachůnková and S. Staněk: Topological degree methods in functional boundary value problems at resonance. Nonlin. Anal. TMA 27 (1996), 271-285. · Zbl 0853.34062
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