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

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.


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
Full Text: DOI


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