On the sign-changing solutions for strong singular one-dimensional p-Laplacian problems with p-superlinearity

We consider the one-dimensional p-Laplacian problem [GRAPHICS] where phi(p)(s) = vertical bar s vertical bar(p-2) s, p > 1, h(t) >= 0 and 0 < integral(I) h(t)dt < infinity for any compact subinterval I subset of (0,1), and f is an element of(R, R) with f p-superlinear at infinity. By applying the global bifurcation argument and nonlinear eigenvalue theory, we establish an existence and multiplicity result of sign-changing solutions for (P). Our result generalizes and improves some recent result from the case h is an element of L-1(0,1) to a strong singular case h is an element of A sic {h is an element of L-loc(1)(0, 1) : integral(1)(0)(s(1 - s))(P-1)h(s)ds < infinity}.