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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.

34N05Dynamic equations on time scales or measure chains
34B09Boundary eigenvalue problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
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