Entire blow-up solutions of semilinear elliptic systems with quadratic gradient terms
Summary: We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms, \(\Delta u_i + |\nabla u_i|^2 = p_i(|x|)f_i(u_1, u_2, \dots, u_d)\) for \(i = 1, 2, \dots, d\) on \(\mathbb R^N, N \geq 3\) and \(d \in \{1, 2, 3, \dots\}\). 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.
scientific article; zbMATH DE number 6134147
scientific article