Uniqueness of positive solutions of a class of O.D.E. with Robin boundary conditions. (English) Zbl 1082.34024
Summary: We study the uniqueness of positive solutions of the boundary value problem
\[
u''+h(t)u'+f(t,u)=0,\;t\in(a,b)\quad u(a)=0,\;u'(b)=0,
\]
where \(0<a<b<\infty\), \(h\in C([0,\infty)\), \(h\in C([0,\infty),\mathbb{R})\) and \(f\in C^1([0,\infty)\times [0,\infty)\times[0,\infty))\) satisfy suitable conditions. The proof of our main result is based upon the shooting method and the Sturm comparison theorem.
MSC:
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
Boundary value problem; Positive solutions; Uniqueness; Shooting method; Sturm comparison theoremReferences:
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