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Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems. (English) Zbl 1215.34035

The authors study the Sturm-Liouville-like boundary value problem

${\left({\varphi }_{p}\left({u}^{\text{'}}\left(t\right)\right)\right)}^{\text{'}}+\psi \left(t\right)f\left(t,u\left(t\right),{u}^{\text{'}}\left(t\right)\right),\phantom{\rule{4pt}{0ex}}0

where ${\varphi }_{p}\left(x\right)={|x|}^{p-2}x$, $p>1$. By using the fixed point theorem of cone expansion and compression of norm type in a cone, the existence of at least one positive symmetric solution is established. It is worth noticing that the nonlinear term contains the first derivative of the unknown function.

MSC:
 34B24 Sturm-Liouville theory 34B18 Positive solutions of nonlinear boundary value problems for ODE 34B10 Nonlocal and multipoint boundary value problems for ODE 47N20 Applications of operator theory to differential and integral equations
References:
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