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On positive solutions of some nonlinear fourth-order beam equations. (English) Zbl 1006.34023
Summary: The existence, uniqueness and multiplicity of positive solutions to the following boundary value problems is considered \[ u^{(4)}(t)- \lambda f(t, u(t))= 0,\quad\text{for }0< t< 1,\quad u(0)= u(1)= u''(0)= u''(1)= 0, \] where \(\lambda> 0\) is a constant, \(f: [0,1]\times [0,+\infty)\to [0,+\infty)\) are continuous.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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