Multiple solutions for second-order three-point boundary value problems with p-Laplacian operator

作者：Guo Yanping; Ji Yude^*; Liu Xiujun

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(7-8): 3517-3529.

DOI：10.1016/j.na.2009.02.015

• Multiple solution
• Generalized polar coordinate
• Boundary value problem
• p-Laplacian operator
• Leray-Schauder degree

In this paper, we study the second-order three-point boundary value problem with a p-Laplacian operator
{(phi(p)(x'(t)))' + g(x(t)) = f (t, x(t), x'(t)), x(0) = 0, x(xi) = beta x(1),
where phi(p)(s) = vertical bar S vertical bar(p-2)s, p > 1, xi is an element of (0, 1), beta is an element of (0, 1) boolean OR (1, infinity). We obtain sufficient conditions for the existence of multiple solutions by applying generalized polar coordinates and the Leray-Schauder degree theorem.

• 出版日期2009-10-1
• 单位河北科技大学