Nontrivial solutions of the asymmetric beam system with jumping nonlinear terms

초록

We investigate the existence of multiple nontrivial solutions (ξ,η) for perturbations b1 [ (u + 2) + - 2 ] and b2 [ (u + 3) - 3 ] of the beam system with Dirichlet boundary condition Lξ = b1 [ (ξ+ 3η + 2) - 2 ] in (- π/ 2, π/ 2) Rdbl;, Lη = b2[ (ξ+ 3η + 3)- 3 ] in (- π/ π2, /2) ×, where u = max { u, 0 }, and μν, are nonzero constants. Here L is the beam operator in ℝ, and the nonlinearity (b1 [ (u + 2) + - 2 ] + b2 [ (u + 3) - 3] crosses the eigenvalues of the beam operator. Copyright © 2010 Tacksun Jung and Q-Heung Choi.