Open Access Research

Ground state and mountain pass solutions for discrete p ( ⋅ ) -Laplacian

Cristian Bereanu1*, Petru Jebelean2 and Călin Şerban2

Author Affiliations

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

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Boundary Value Problems 2012, 2012:104 doi:10.1186/1687-2770-2012-104

Published: 19 September 2012

Abstract

In this paper we study the existence of solutions for discrete <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/104/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/104/mathml/M3">View MathML</a>-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.

Keywords:
discrete <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/104/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/104/mathml/M3">View MathML</a>-Laplacian operator; variational methods; critical point; Palais-Smale condition; Mountain Pass Theorem