Multiplicity of Solutions for the Perturbed Fourth-Order Elliptic Equations of Kirchhoff Type

Project: National Science and Technology CouncilNational Science and Technology Council Academic Grants

Project Details


In this project, we will investigate the existence of multiple solutions for the fourth order elliptic equations of Kirchhoff type. $\Delta^{2}u-M(\int_{\Omega}\left\vert \nabla u\right\vert ^{2}dx)\Delta u+\rho u=\lambda f(x,u)$ in $\Omega$We consider that this equation is in a bounded domain with smooth boundary, and M:R+-> R is a continuous function.Actually, the weak solution of this equation is the critical point of the associated energy functional J.We would like to study Mountain pass theorem, Palais-Smale theory and the methods of Tarantello’s paper to improve our results.Since energy functional J is not bounded from below in H, then we consider the Nehari manifold M that contains all nontrivial weaksolutions of this problem, and we have that J is coercive and bounded from below on M.Next, under some assumptions, we will prove the existence of the ground state solution and higher energy solution for this equation.Besides, it is related to the travelling waves in suspension bridges.

Project IDs

Project ID:PA10708-1084
External Project ID:MOST107-2115-M182-001
Effective start/end date01/08/1831/07/19


  • Fourth order elliptic equations
  • perturbation
  • Mountain pass theorem
  • Palais-Smale theory


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