## 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.

### 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
Full Text:

### References:

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