## Countably many solutions of a fourth order boundary value problem.(English)Zbl 1072.34018

Summary: We apply fixed-point theorems to obtain sufficient conditions for the existence of infinitely many solutions of the nonlinear fourth-order boundary value problem $u^{(4)}(t) = a(t)f(u(t)), \quad 0 < t < 1, \qquad u(0) = u(1) = u'(0) = u'(1) = 0,$ where $$a(t)$$ is $$L^p$$-integrable and $$f$$ satisfies certain growth conditions.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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