C1-regularity of solutions for p-Laplacian problems

In this work, we study C 1 -regularity of solutions for one-dimensional p -Laplacian problems and systems with a singular weight which may not be in L 1 . On the basis of the regularity result, we give an example to show the multiplicity of positive (or negative) solutions as well as sign-changing solutions especially when the nonlinear term is p -superlinear.