Triple positive solutions for boundary value problems on infinite intervals. (English) Zbl 1128.34011

Lian, Hairong; Pang, Huihui; Ge, Weigao

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 7, 2199-2207 (2007).

The article is devoted to Sturm-Liouville boundary value problems for second-order nonlinear ordinary differential equations with a \(p\)-Laplacian on a half line: \[ (\varphi_p(x'(t)))'+\phi(t)f(t,x(t),x'(t))=0,\;0< t<+\infty; \]
\[ \alpha x(0)-\beta x'(0)=0,\;x'(\infty)=0. \] Here, \(\varphi_p (s)=|s|^{p-2}s\), \(p>1\), the functions \(\phi:\mathbb R_+\to \mathbb R_+\), \(f:\mathbb R^3_+\to\mathbb R_+\) are continuous, \(\alpha>0\), \(\beta \geq 0\). Sufficient conditions are obtained for the existence of at least three positive solutions. The proofs are based on fixed point considerations. An example is given.

Reviewer: Sergei A. Brykalov (Ekaterinburg)

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B40	Boundary value problems on infinite intervals for ordinary differential equations
34B24	Sturm-Liouville theory

Keywords:

multiplicity; fixed point theory; half line

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