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Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces. (English) Zbl 1159.34020
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.

##### MSC:
 34B18 Positive solutions of nonlinear boundary value problems for ODE 34B15 Nonlinear boundary value problems for ODE 34G20 Nonlinear ODE in abstract spaces
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##### References:
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