Multiple solutions of Sturm-Liouville boundary value problem via lower and upper solutions and variational methods

作者：Tian, Yu^*; Ge, Weigao

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(17): 6733-6746.

DOI：10.1016/j.na.2011.06.053

• Multiple solutions
• Sturm-Liouville boundary value problem
• Critical point
• Lower and upper solutions
• Variational methods

In this paper, we prove the existence of multiple solutions for second order Sturm-Liouville boundary value problem
{-Lu = f (x, u), x is an element of [0, 1] R(1)(u) = 0, R(2)(u) = 0,
where Lu = (p(x)u')' - q(x) u is a Sturm-Liouville operator, R(1)(u) = alpha u'(0) - beta u(0), R(2)(u) = gamma u'(1)+sigma u(1). The technical approach is fully based on lower and upper solutions and variational methods. The interesting point is that the existence of four solutions and seven solutions is given.

• 出版日期2011-12
• 单位北京理工大学; 北京邮电大学