Nondegeneracy of positive solutions to homogeneous second-order differential systems and its applications. (English) Zbl 1199.34090

Dai, Qiuyi; Tisdell, Christopher C.

Acta Math. Sci., Ser. B, Engl. Ed. 29, No. 2, 435-446 (2009).

Summary: This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B05	Linear boundary value problems for ordinary differential equations

Keywords:

second-order ordinary differential system; Dirichlet problem; positive solution; nondegeneracy; multiplicity