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Kết quả tồn tại cho bài toán Dirichlet bị nhiễu mà không có điều kiện dấu trong không gian Orlicz
Tóm tắt
Chúng tôi nghiên cứu kết quả tồn tại cho các phương trình elliptic phi tuyến dạng Au + g(x, u, ∇u) = f, trong đó thuật ngữ –div (a(x, u, ∇u)) là một toán tử Leray–Lions từ một tập con của
$$ {W}_0^1{L}_M\left(\Omega \right) $$
vào đối ngẫu của nó. Các điều kiện tăng trưởng và cưỡng chế trên trường véc tơ đơn điệu a được quy định bởi một hàm N, mà không nhất thiết phải thoả mãn điều kiện Δ2. Do đó, chúng tôi sử dụng các không gian Orlicz–Sobolev không nhất thiết là phản chiếu và giả sử rằng sự phi tuyến g(x, u, ∇u) là một hàm Carathéodory chỉ thoả mãn điều kiện tăng trưởng mà không có điều kiện dấu. Phía bên phải f thuộc về
$$ {W}^{-1}{L}_{\overline{M}}\left(\Omega \right). $$
Từ khóa
#phương trình elliptic phi tuyến #toán tử Leray–Lions #không gian Orlicz #hàm Carathéodory #điều kiện tăng trưởngTài liệu tham khảo
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