The Existence of Positive Solutions for Third-Order p-Laplacian m-Point Boundary Value Problems with Sign Changing Nonlinearity on Time Scales
نویسندگان
چکیده
We study the following third-order p-Laplacian m-point boundary value problems on time scales φp uΔ∇ ∇ a t f t, u t 0, t ∈ 0, T T , u 0 ∑m−2 i 1 biu ξi , u Δ T 0, φp uΔ∇ 0 ∑m−2 i 1 ciφp u Δ∇ ξi , where φp s is p-Laplacian operator, that is, φp s |s|p−2s, p > 1, φ−1 p φq, 1/p 1/q 1, 0 < ξ1 < · · · < ξm−2 < ρ T . We obtain the existence of positive solutions by using fixed-point theorem in cones. In particular, the nonlinear term f t, u is allowed to change sign. The conclusions in this paper essentially extend and improve the known results.
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