The solvability of nonhomogeneous boundary value problems with ϕ-Laplacian operator
1 Department of Mathematics, Ningbo University, Ningbo, 315211, P.R. China
2 Basic Science Department, Tianjin Agricultural University, Tianjin, 300384, P.R. China
Boundary Value Problems 2014, 2014:82 doi:10.1186/1687-2770-2014-82Published: 10 April 2014
We treat the nonhomogeneous boundary value problems with ϕ-Laplacian operator , , , , where () is an increasing homeomorphism such that , , , , , and is continuous. We will show that even if some of the τ and are negative, the boundary value problem with singular ϕ-Laplacian operator is always solvable, and the problem with a bounded ϕ-Laplacian operator has at least one positive solution.