The existence of positive pseudo-symmetric solutions to a four-point boundary value problem with \(p\)-Laplacian-like operator on time scales (Q1032565)

The authors study the existence of a positive solution to the second order \(p\)-Laplacian dynamic equation \[ \big(\Phi(u^\Delta(t))\big)^\nabla+q(t)\,f(t,u(t),u^\Delta(t))=0 \] with some pseudo-symmetric boundary conditions. The pseudo-symmetry of the time scale \({\mathbb T}\) means that if \(a,b\in{\mathbb T}\), \(a<b\), then \(t\in[a,b]\cap{\mathbb T}\) implies \(a+b-t\in[a,b]\cap{\mathbb T}\). The fixed point theorem of Leray-Schauder is used for the proof.