A critical points approach for the existence of multiple solutions of a Dirichlet quasilinear system

作者：Graef John R^*; Heidarkhani Shapour; Kong Lingju

来源：Journal of Mathematical Analysis and Applications, 2012, 388(2): 1268-1278.

DOI：10.1016/j.jmaa.2011.11.019

• Three solutions
• Critical point
• Multiplicity results
• Dirichlet problem

In this paper, we establish the existence of at least three classical solutions for the Dirichlet quasilinear elliptic system
{-(p(i) - 1)vertical bar u'(i)(x)vertical bar(pi-2) u ''(i)(x)
= [lambda F(ui)(x, u(1), ... , u(n)) + mu G(ui) (x, u(1), ... , u(n))h(i)(x, u'(i)), x is an element of (a, b),
u(i) (a) = u(i)(b) = 0, for i = 1, ... , n.
Our main tool is a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal. 70 (2009) 3084-3089].

• 出版日期2012-4-15