带有非局部项的四阶椭圆型方程组的无穷多高能量解的存在性
High Energy solutions of Forth-Order Elliptic Systems Involving Nonlocal Term and Sign-Changing Potential
摘要:

该文主要研究如下含变号位势和非局部项的四阶椭圆方程组

其中Δ2=Δ（Δ）是重调和算子，V（x）∈C（ ℝ3，ℝ），F（x，u，v ）∈C1（ℝ3xℝxℝ,ℝ），V（x）为变号函数，Fu=∂F/∂u，Fv=∂F/∂v。在满足一定条件下，利用Fountain定理证明了该问题存在无穷多高能量解。

Abstract: This paper focus on the following forth-order elliptic equations involving non-local terms and

sign-changing potential

Where Δ2=Δ(Δ) is the biharmonic operator, V(x)∈C( ℝ3,ℝ), F(x,u,v )∈C1(ℝ3xℝxℝ,ℝ). V(x) is sign-changing function, Fu=∂F/∂u, Fv=∂F/∂v. Under certain conditions, it’s proved that there are infinitely many high-energy solutions to the problem using Fountain Theorem.

文章引用：钱雅雯, 贾高. 带有非局部项的四阶椭圆型方程组的无穷多高能量解的存在性[J]. 应用数学进展, 2019, 8(12): 1943-1952. https://doi.org/10.12677/AAM.2019.812223

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