Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight

作者：Zhang, Guoqing; Yao, Ziyan^*

来源：Abstract and Applied Analysis, 2014, 2014: 942092.

DOI：10.1155/2014/942092

• EXISTENCE

Using the suitable Trudinger- Moser inequality and the Mountain PassTheorem, we prove the existence of multiple solutions for a class of N-Laplacian equations with critical growth and indefinite weight -div(vertical bar del vertical bar(N-2) del u) + V(x)vertical bar u vertical bar(N-2)u = lambda vertical bar u vertical bar(N-2)u/vertical bar x vertical bar(beta)) + (f(x,u)/vertical bar x vertical bar(beta) +epsilon h(x), x epsilon RN, u not equal 0, x epsilon R-N, where 0 < beta < N, V(x) is an indefinite weight f : R-N x R -> R behaves like exp(alpha vertical bar u vertical bar(N/N(N-1))) and does not satisfy the Ambrosetti- Rabinowitz condition, and h epsilon (W-1,W-N(R-N))*.

• 出版日期2014
• 单位上海理工大学