MULTIPLE SOLUTIONS FOR A KIRCHHOFF EQUATION WITH NONLINEARITY HAVING ARBITRARY GROWTH

作者：Furtado Marcelo F^*; Zanata Henrique R

来源：Bulletin of the Australian Mathematical Society, 2017, 96(1): 98-109.

DOI：10.1017/S0004972717000144

• Kirchhoff equation
• infinitely many solutions
• variational method
• truncation argument

We prove the existence of infinitely many solutions u is an element of W-0(1,2) (Omega) for the Kirchho ff equation
-(alpha+ beta integral(Omega) vertical bar del u vertical bar(2) dx)Delta u = a(x) vertical bar u vertical bar(q) (1)u + mu f ( x, u) in Omega,
where Omega subset of R-N is a bounded smooth domain, a(x) is a (possibly) sign-changing potential, 0 < q < 1, alpha > 0, beta >= 0, mu > 0 and the function f has arbitrary growth at infinity. In the proof, we apply variational methods together with a truncation argument.

• 出版日期2017-8