MULTIPLE POSITIVE SOLUTIONS FOR ELLIPTIC PROBLEM WITH CONCAVE AND CONVEX NONLINEARITIES

作者：Liu, Jiayin^*; Zhao, Lin; Zhao, Peihao

来源：Electronic Journal of Differential Equations, 2015, 78.

• Variational methods
• supercritical exponent
• mountain pass theorem
• Moser iteration technique

In this article, we consider the existence of multiple solutions to the elliptic problem
-Delta u = lambda u(q) + u(s) + mu u(P) in Omega,
u > 0 in Omega,
u = 0 on partial derivative Omega,
where Omega subset of R-N (N >= 3) is a bounded domain with smooth boundary Omega partial derivative, o <q < 1 < s < 2* - 1 <= p, 2* := 2N/N-2 lambda and mu are nonnegative parameters. By using variational methods, truncation and Moser iteration techniques, we show that if the parameters A and p are small enough, then the problem has at least two positive solutions.

• 出版日期2015-3-31
• 单位兰州大学; 中国矿业大学（北京）