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Existence of a solution and a positive solution of a boundary value problem for a nonlinear fourth-order dynamic equation. (English) Zbl 1152.34322
Summary: By using the Schauder fixed point theorem, we offer some existence criteria for a solution and a positive solution to the following fourth-order two-point boundary value problem on time scale $\Bbb T$: $$u^{\Delta\Delta\Delta\Delta}(t)= f(t,u(t), u^{\Delta\Delta}(t))= 0, \quad t\in [a,\rho^2(b)],$$ $$u(a)=A, \quad u(\sigma^2(b))=B, \quad u^{\Delta\Delta}(a)= C, \quad u^{\Delta\Delta}(b)=D,$$ where $a,b\in\Bbb T$ and $a<b$.

MSC:
34B15Nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
39A10Additive difference equations
47N20Applications of operator theory to differential and integral equations
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References:
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