MULTIPLE POSITIVE SOLUTIONS FOR DISCRETE p-LAPLACIAN EQUATIONS WITH POTENTIAL TERM

作者：Kim Jong Ho^*; Park Jea Hyun; Lee June Yub

来源：Applicable Analysis and Discrete Mathematics, 2013, 7(2): 327-342.

DOI：10.2298/AADM130612012K

• Discrete boundary value problems
• discrete p-Laplacian
• graph Laplacian
• multiple solutions

We study the existence of solutions to nonlinear discrete boundary value problems with the discrete p-Laplacian, potential, and nonlinear source terms. Using variational methods, we demonstrate that there exist at least two positive solutions. The existence strongly depends on the smallest positive eigenvalue of Dirichlet eigenvalue problems and the growth conditions of the source terms.

• 出版日期2013-10