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A note on the singular Sturm-Liouville problem with infinitely many solutions. (English) Zbl 1026.34023
Here, the author investigates the nonlinear boundary value problem \[ -u''(t)= a(t)f\bigl[ u(t)\bigr], \quad 0<t<1, \]
\[ \alpha u(0)-\beta u'(0)=0, \quad \gamma u(1)+ \delta u'(1)=0, \] where \(\alpha,\beta, \gamma, \delta \geq 0\), \(\alpha\gamma +\alpha\delta +\beta\gamma >0\) and \(a(t)\) is in a class of singular functions.
Under certain growth condition imposed on \(f(u)\), the author obtains infinitely many solutions to the problem.
The main tools used in this paper are the Kramel’skij fixed-point theorem and the Hölder inequality.

MSC:
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B24 Sturm-Liouville theory
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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