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Positive solutions to boundary value problems with nonlinear boundary conditions. (English) Zbl 1237.34153
The author considers the boundary value problem $y^{\Delta\Delta}=-\lambda f(t,y^\sigma(t)),$ subject to the boundary conditions $y(a)=\phi(y) \text{ and }y(\sigma^2(b))=0.$ They give the form of solutions of the boundary value problem, and apply cone theoretic tools to prove that the problem has at least one positive solution. At the end of this paper, some examples are worked out to illustrate the main results.

##### MSC:
 34N05 Dynamic equations on time scales or measure chains 34B09 Boundary eigenvalue problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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