We are concerned with a four-point boundary-value problem of the $p$-Laplacian dynamic equation on time scales where the nonlinear term contains the first-order derivatives of the dependent variable. By using Krasnosel'skii's fixed-point theorem, some new sufficient conditions are obtained for the existence of at least single or twin positive pseudo-symmetric solutions to this problem. We also establish the existence of at least triple or arbitrary odd positive pseudo-symmetric solutions to this problem by using the Avery-Peterson fixed-point theorem. As applications, two examples are given to illustrate and explain our main results.
Zhaosheng Feng. You-hui Su. "Existence of pseudo-symmetric solutions to a $p$-Laplacian four-point BVPs involving derivatives on time scales." Differential Integral Equations 25 (5/6) 441 - 466, May/June 2012. https://doi.org/10.57262/die/1356012674