Large Solutions Of Semilinear Elliptic Equations With Nonlinear Gradient Terms

In this paper, we study the existence of the large solutions for semilinear elliptic value problem of second order with gradient terms:Δu±|u|^q=p(x)f(u),u>0,x∈Ωu|_Ω=∞ (P±)by the skill of inequality, approximation method combined with the regular theory and inner estimate theory of elliptic equation of second order, where q∈[0, 2). we obtained the corresponding results in the following five directions:(i) The existence of the positive large solutions of the problem (P+), where Ω is a bounded smooth domain in R^N(N>=3) and the coefficient p(x) is bounded on Ω.(ii) The existence of the entire large solutions of the problem (P+), where Ω=R^N(N>=3) and the coefficient p(x) satisfies certain delay conditions. (iii) The existence of the positive large solutions of the problem (P-), where ( is a bounded smooth domain in R^N(N>=3) and the coefficient p(x) is bounded on Ω. (iv) The existence of the entire large solutions of the problem (P-), where Ω=R^N (N>=3) and we require that t^2+βφ(t)f(t^α) be bounded above for some positive β and α.. (V) The nonexistence of the large solutions of the problem (P+).The main results of this paper extend the results of Alan V. Lair and Aihua W. Wood [3], and include the main results in [1], [2], [13].