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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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