Existence results of sign-changing solutions for singular one-dimensional [formula omitted]-Laplacian problems

Abstract

Consider singular one-dimensional p -Laplacian problems with Dirichlet boundary condition { ( φ p ( u ′ ( t ) ) ) ′ + h ( t ) f ( u ( t ) ) = 0 , t ∈ ( 0 , 1 ) , ( P ) u ( 0 ) = 0 = u ( 1 ) , ( D ) where φ p : R → R is defined by φ p ( x ) = | x | p − 2 x , p > 1 , h a nonnegative measurable function on ( 0 , 1 ) which may be singular at t = 0 and/or t = 1 and 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 ) .