# zbMATH — the first resource for mathematics

Existence of positive solutions to vector boundary value problems I. (English) Zbl 0952.34017
The author deals with a second-order $$n$$-dimensional vector differential system with Dirichlet boundary value conditions. A sufficient condition is given for definition intervals that guarantees the existence of a positive solution to the differential system when some other assumptions of the differential system are fulfilled. The proof of the main result is based on some auxiliary lemmas and on the Brouwer degree of mappings. This paper is the first part of the author’s work on this problem.

##### MSC:
 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
##### Keywords:
shooting method; positive solution; Brouwer degree
Full Text:
##### References:
 [1] BEBERNES J. W.: Periodic boundary value problems for systems of second order differential equations. J. Differential Equations 13 (1973), 32-47. · Zbl 0284.34016 [2] FECKAN M.: Positive solutions of a certain type of two-point boundary value problem. Math. Slovaca41 (1991), 179-187. [3] FULIER J.: On a nonlinear two-point boundary value problem. Acta Math. Univ. Comenian. LVIII-LIX (1990), 17-35. · Zbl 0729.34015 [4] GAINES R. E.-SANTANILLA J.: A coincidence theorem in convex sets with applications to periodic solutions of ordinary differential equations. Rocky Mountain J. Math. 12 (1982), 669-678. · Zbl 0508.34030 [5] GREGUS M.-SVEC M.-SEDA V.: Ordinary Differential Equations. Alfa, Bratislava, 1985. [6] HALE J. K.: Ordinary Differential Equations. Wiley-Interscience, New York, 1969. · Zbl 0186.40901 [7] NIETO J. J.: Existence of solutions in a cone for nonlinear alternative problems. Proc. Amer. Math. Soc. 94 (1985), 433-436. · Zbl 0585.47050
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.