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Nhiều Giải Pháp Năng Lượng Cao cho Phương Trình Bậc Tư Kiểu Kirchhoff Trong ℝN
Tóm tắt
Trong bài báo này, chúng tôi nghiên cứu các phương trình elliptic bậc tư của loại Kirchhoff sau đây
$$\Delta^2u - (a+b\int_{\mathbb{R}^N} | \triangledown u|^2dx)\Delta u + V(x)u=f(x, u), \;\;x\in\mathbb{R}^N,$$
trong đó Δ2 := Δ(Δ) là toán tử biharmonic, a, b > 0 là các hằng số, V ∈ C(ℝN, ℝ) và f ∈ C(ℝN × ℝ, ℝ). Dưới một số giả thiết thích hợp về V(x) và f(x, u), những kết quả mới về sự tồn tại của vô số nghiệm năng lượng cao cho phương trình trên được thu được thông qua Định lý Đường Diệt Duyệt Đối Xứng.
Từ khóa
#phương trình Kirchhoff #phương trình elliptic #nghiệm năng lượng cao #toán tử biharmonic #Định lý Đường Diệt Duyệt Đối XứngTài liệu tham khảo
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