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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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