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Zbl 1159.34020
Zhang, Xuemei; Feng, Meiqiang; Ge, Weigao
Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 69, No. 10, A, 3310-3321 (2008). ISSN 0362-546X

The paper deals with the existence of positive solutions of the boundary value problem $$x^{(4)}-\lambda f(t,x)=\theta, \quad 0<t<1$$ in a Banach space $E$ under the boundary conditions $$x(0)=x(1)= \int_0^1g(s)x(s)\,ds \quad\text{and}\quad x''(0)=x''(1)= \int_0^1h(s)x''(s)\,ds.$$ The authors prove their results by using a cone in $E$ and applying the fixed point theory in cones for strict set contraction operators. An example is given to illustrate the result.
[George Karakostas (Ioannina)]
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE
34G20 Nonlinear ODE in abstract spaces

Keywords: boundary value problem; positive solutions; fixed point index theory.

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