Ground state and mountain pass solutions for discrete
1 Institute of Mathematics “Simion Stoilow”, Romanian Academy, 21, Calea Griviţei, Sector 1, Bucharest, RO-010702, Romania
2 Department of Mathematics, West University of Timişoara, 4, Blvd. V. Pârvan, Timişoara, RO-300223, Romania
Boundary Value Problems 2012, 2012:104 doi:10.1186/1687-2770-2012-104Published: 19 September 2012
In this paper we study the existence of solutions for discrete -Laplacian equations subjected to a potential type boundary condition. Our approach relies on Szulkin’s critical point theory and enables us to obtain the existence of ground state as well as mountain pass type solutions.
MSC: 39A12, 39A70, 49J40, 65Q10.