Non-trivial solutions for a semilinear biharmonic problem with critical growth and potential vanishing at infinity

作者：Deng, Yinbin^*; Shuai, Wei

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2015, 145(2): 281-299.

DOI：10.1017/S0308210513001170

• NONLINEAR SCHRODINGER-EQUATIONS
• POSITIVE SOLUTIONS
• ELLIPTIC EQUATION
• EXISTENCE

In this paper, we study the existence of non-trivial solutions for the following class of semilinear biharmonic problem with critical nonlinearity: @@@ Delta(2)u + V (x) u = mu K(x)f(u) + P(x)|u|(2**-2)u, x is an element of R-N, u is an element of D-2,D-2(R-N). @@@ Here Delta(2)u = Delta(Delta u), N >= 5, mu > 0 is a parameter, 2** = 2N/(N - 4) is the critical Sobolev exponent, V (x) and K(x) are positive continuous functions that vanish at infinity, f is a function with a subcritical growth and P(x) is a bounded, non-negative continuous function. By working in weighted Sobolev spaces and using a variational method, we prove that the problem has at least one non-trivial solution.

• 出版日期2015-4
• 单位华中师范大学