Nontrivial Solutions of the Asymmetric Beam System with Jumping Nonlinear Terms. (21st September 2010) - Jung Jung, Tacksun Tacksun; Choi Choi, Q-Heung Q-Heung
Abstract : We investigate the existence of multiple nontrivial solutions ( ξ, η ) for perturbations b 1 [ ( u + 2 ) + - 2 ] and b 2 [ ( u + 3 ) + - 3 ] of the beam system with Dirichlet boundary condition L ξ = b 1 [ ( ξ + 3 η + 2 ) + - 2 ] in ( - π / 2, π / 2 ) × ℝ, L η = b 2 [ ( ξ + 3 η + 3 ) + - 3 ] in ( - π / 2, π / 2 ) × ℝ, where u + = max u, 0 , and μ, ν are nonzero constants. Here L is the beam operator in ℝ 2, and the nonlinearity ( b 1 [ ( u + 2 ) + - 2 ] + b 2 [ ( u + 3 ) + - 3 ] crosses the eigenvalues of the beam operator.