Positive solutions for classes of multi-parameter fourth-order impulsive differential equations with one-dimensional singular p-Laplacian

The authors consider the following impulsive differential equations involving the one-dimensional singular p-Laplacian: (phi(p)(y"(t)))" = lambda omega(t)f(t,y(t)), t is an element of J, t not equal t(k), k = 1,2, ... , m, Delta y'vertical bar(t=tk) = -mu I-k(t(k), y(t(k))), k = 1,2, ... , m, ay(0) - by'(0) = integral(1)(0) 0 h(s) y(s) ds, ay(1) + by'(1) = integral(1)(0) h(s) y(s) ds, phi(p)(y"(0)) = phi(p)(y"(1)) = integral(1)(0) h(t)phi(p)(y"(t)) dt, where lambda > 0 and mu > 0 are two parameters. Several new and more general existence and multiplicity results are derived in terms of different values of lambda > 0 and mu > 0. In this case, our results cover equations without impulsive effects and are compared with some recent results.