×

On four-point regular BVPs for second-order quasi-linear ODEs. (English) Zbl 0769.34019

The authors consider the scalar four-point boundary value problem of the form \(x''=f(t,x,x')\), \(x(a)+px(b)=A\), \(x(c)+qx(d)=B\), where \(A,B,a,b,c\in\mathbb{R}\), \(p,q\in\{-1,0,1\}\) and \(f\) is supposed to be continuous. They prove the existence of solutions using Green’s functions and the Schauder fixed point theorem.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: EuDML

References:

[1] J. Andres: A four-point boundary value problem for the second-order ordinary differential equations. Arch. Math. (Basel) 53 (1989), 384-389. · Zbl 0667.34024
[2] I. Bihari: Notes on a nonlinear integral equation. Stud. Sci. Math. Hung. 2 (1967), 1-6. · Zbl 0147.10302
[3] L. Collatz: Funkcionální analýza a numerická matematika. SNTL, Praha 1970.
[4] A. G. Lomtatidze: On a singular three-point boundary value problem. Trudy IPM Tbilisi 17 (1986), 122-134 · Zbl 0632.34011
[5] M. A. Neumark: Lineare Differentialoperatoren. VEB DVW, Berlin 1960. · Zbl 0092.07902
[6] I. Rachůnková: A four-point problem for ordinary differential equations of the second order. Arch. Math. (Brno) 25, 4 (1989), 175-184. · Zbl 0715.34033
[7] I. Rachůnková: Existence and uniqueness of solutions of four-point boundary value problems for 2nd order differential equations. Czech. Math. J. 39 (1989), 692-700. · Zbl 0695.34016
[8] G. F. Roach: Green’s functions. Cambridge Univ. Press, Cambridge 1982. · Zbl 0522.65075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.