Positive solutions for nonlinear three-point boundary value problems on time scales

By Hong‐Rui Sun, Wan-Tong Li. 2004

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Abstract Let T be a time scale such that 0 , T ∈ T . Consider the following three-point boundary value problem on time scales: u Δ ∇ ( t ) + a ( t ) f ( t , u ( t ) ) = 0 , t ∈ ( 0 , T ) , β u ( 0 ) − γ u Δ ( 0 ) = 0 , α u ( η ) = u ( T ) , where β , γ ⩾ 0 , β + γ > 0 , η ∈ ( 0 , ρ ( T ) ) , 0 α T / η , and d = β ( T − α η ) + γ ( 1 − α ) > 0 . By using fixed point theorems in cones, some new and general results are obtained for the existence of single and multiple positive solutions of the above problem. In particular, our criteria generalize and improve some known results.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/db92dfada751c6df957bf9c5714f989471842991