Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms. (2nd December 2012)

• Record Type: Journal Article
• Authors: Yang, Yongju; Zhang, Xinguang
• Other Names: Wu Yong Hong Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-12-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/697565
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms, Δ u i + | ∇ u i | 2 = p i ( | x | ) f i ( u 1, u 2, …, u d ) for i = 1, 2, …, d on R N, N ≥ 3 and d ∈ { 1, 2, 3, … } . We establish the conditions on p i that ensure the existence of nonnegative radial solutions blowing up at infinity and also the conditions for bounded solutions on the entire space. The condition on f i is simple and different to the Keller-Osserman condition.