## Existence of multiple positive solutions for Sturm-Liouville-like four-point boundary value problem with $$p$$-Laplacian.(English)Zbl 1145.34309

Summary: We consider the Sturm-Liouville-like four-point boundary value problem with $$p$$-Laplacian
\begin{aligned} & (\phi_p(u'))'(t)+f(t,u(t))=0,\quad t\in (0,1),\\ & u(0)-\alpha u'(\xi)=0,\quad u(1)+\beta u'(\eta)=0,\end{aligned}
where $$\phi_p(s)=|s|^{p-2}s$$, $$p>1$$. By means of a fixed-point theorem for operators on a cone, the existence of multiple (at least three) positive solutions to the above boundary value problem is obtained.

### MSC:

 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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### References:

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