Existence results of sign-changing solutions for singular one-dimensional image-Laplacian problems Original Research Article

Consider singular one-dimensional pp-Laplacian problems with Dirichlet boundary condition View the MathML source{(φp(u′(t)))′+h(t)f(u(t))=0,t∈(0,1),(P)u(0)=0=u(1),(D) Turn MathJax on where φp:R→Rφp:R→R is defined by φp(x)=|x|p−2x,p>1,hφp(x)=|x|p−2x,p>1,h a nonnegative measurable function on (0,1)(0,1) which may be singular at t=0t=0 and/or t=1t=1 and f∈C(R,R)f∈C(R,R). By applying the global bifurcation theorem and deriving the shape of the unbounded subcontinua of solutions, we obtain the existence and multiplicity results of sign-changing solutions for (P)+(D)(P)+(D).