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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

(φ p (u ' (t))) ' +ψ(t)f(t,u(t),u ' (t)),0<t<1,u(0)-αu ' (ξ)=0,u(1)+αu ' (η)=0,(P)

where φ p (x)=|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:
34B24Sturm-Liouville theory
34B18Positive solutions of nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
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