## 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

### Keywords:

existence; uniqueness; multiplicity; positive solutions
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### References:

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