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

Kosmatov, Nickolai

Electron. J. Qual. Theory Differ. Equ. 2004, Paper No. 12, 15 p. (2004).

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