Homoclinic solutions for a nonlinear second order differential system with [formula omitted]-Laplacian operator

Abstract

The author of this paper studies the existence of local minimum point of functional φ in the first, and then the existence of homoclinic solutions to a p -Laplacian system d d t [ | u ′ ( t ) | p − 2 u ′ ( t ) ] = ∇ F ( t , u ( t ) ) + f ( t ) is investigated. Under local condition F ( t , x ) ≥ F ( t , 0 ) + b 0 | x | μ for all ( t , x ) ∈ R × R n with | x | ≤ ρ , where b 0 > 0 , ρ > 0 and μ > 1 are constants, some new results are obtained.