Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation

Abstract In this paper, using the mountain pass theorem, we give the existence result for nontrivial solutions for a class of asymptotically linear fourth-order elliptic equations.

[1]  W. Walter,et al.  Travelling waves in a suspension bridge , 1990 .

[2]  Jihui Zhang,et al.  Existence results for some fourth-order nonlinear elliptic problems of local superlinearity and sublinearity , 2003 .

[3]  Three solutions of a fourth order elliptic problem via variational theorems of mixed type , 2000 .

[4]  A. Pistoia,et al.  Nontrivial solutions for some fourth order semilinear elliptic problems 1 1 Supported by M.P.I. (Res , 1998 .

[5]  Huan-Song Zhou,et al.  Applying the mountain pass theorem to an asymptotically linear elliptic equation on RN , 1999 .

[6]  Y. Chen,et al.  Traveling Waves in a Nonlinearly Suspended Beam: Theoretical Results and Numerical Observations , 1997 .

[7]  Gabriella Tarantello,et al.  A note on a semilinear elliptic problem , 1992, Differential and Integral Equations.

[8]  Huan-Song Zhou.  Existence of asymtotically linear Dirichlet problem , 2001 .

[9]  Alan C. Lazer,et al.  Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis , 1990, SIAM Rev..

[10]  Zhang Ji-hui.  Existence results for some fourth-order nonlinear elliptic problems , 2001 .

[11]  P. J. McKenna,et al.  Global Bifurcation and a Theorem of Tarantello , 1994 .

[12]  C. V. Pao,et al.  On fourth-order elliptic boundary value problems , 1999 .

[13]  Huan-Song Zhou,et al.  Multiple Solutions to p‐Laplacian Problems with Asymptotic Nonlinearity as up−1 at Infinity , 2002 .

[14]  Angela Pistoia,et al.  Multiplicity results for a fourth-order semilinear elliptic problem , 1998 .