A generalization of an extensible beam equation with critical growth in R-N

作者：Cabada Alberto; Figueiredo Giovany M^*

来源：Nonlinear Analysis: Real World Applications , 2014, 20: 134-142.

DOI：10.1016/j.nonrwa.2014.05.005

• Beam equation
• Critical exponent
• Variational methods

In this work we obtain an existence result for a generalized extensible beam equation with critical growth in R-N of the type %26lt;br%26gt;Delta(2)u - M(integral(RN) vertical bar del u vertical bar(2) dx) Delta u + u = lambda f(u) + vertical bar u vertical bar(2**-2)u in R-N %26lt;br%26gt;where N %26gt;= 5 and lambda %26gt; 0. The functions M : [0, +infinity) -%26gt; R and f : R -%26gt; R are continuous. Since there is a competition between the function M and the critical exponent given by 2** = 2N/N-4, we need to make a truncation on function M. Using the size of lambda, we show that each solution of auxiliary problem is a solution of original problem. Our approach is variational and uses minimax point critical theorems.

• 出版日期2014-12