SOLUTIONS TO KIRCHHOFF EQUATIONS WITH COMBINED NONLINEARITIES

作者：Ding, Ling^*; Li, Lin; Zhang, Jing-Ling

来源：Electronic Journal of Differential Equations, 2014, 10.

• Kirchhoff equation
• asymptotically linear
• asymptotically 3-linear
• positive solution
• mountain pass lemma

We prove the existence of multiple positive solutions for the Kirchhoff equation
-(a + b)integral(Omega)vertical bar del u vertical bar(2)dx)Delta u = h(x)u(q) + f (x, u), x is an element of Omega,
u = 0, x is an element of partial derivative Omega,
Here Omega is an open bounded domain in R-N (N = 1, 2, 3), h(x) is an element of L-infinity(Omega) f (x, s) is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. Our main tools are the Ekeland's variational principle and the mountain pass lemma.

• 出版日期2014-1-7
• 单位湖北文理学院; 西南大学