## Existence of three positive solutions for $$m$$-point boundary value problems on infinite intervals.(English)Zbl 1172.34310

Summary: By using the Avery-Peterson fixed point theorem on a cone, we establish the existence of three positive solutions for the boundary value problem
$\big(\varphi_p(x'(t))\big)'+ \phi(t)f(t,x(t),x'(t))=0, \quad 0<t<+\infty,$
$x(0)= \sum_{i=1}^{m-2} \alpha_ix'(\eta_i), \quad \lim_{t\to+\infty} x'(t)=0,$
where $$\varphi_p(s)= |s|^{p-2}s$$, $$p>1$$, $$\phi:\mathbb R_+\to\mathbb R_+$$, $$f(t,u,v):\mathbb R_+\to\mathbb R_+$$ is a continuous function, $$\mathbb R_+=[0,+\infty)$$, $$\alpha_i\geq 0$$ and $$0<\eta_1<\eta_2<\cdots< \eta_{m-2}<+\infty$$ are given.

### MSC:

 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B40 Boundary value problems on infinite intervals for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
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