Some Research Into Existence Of Positive Entire Solutions For A Class Of Quasilinear Elliptic Equations

In this paper, our main purpose is to establish the existence of positive entire solution ofwith super and lower solution. method. On the other hand, we will also prove that there exists the solution of - div(|(?)u|^p-2(?)u) = a(x)(u^m +λuⁿ), x∈R^N, N≥3 .The main contents are as follows:In chapter 2, we study the positive solutionswhere u→f(x,u) is not assumed to be regular near u = 0 and f(x, u) may be more general involving singular, sublinear and superlinear terms..In chapter 3, we studywhere 0 < m < p - 1 < n, a(x)≥0, a(x) not identically zero. Under the condition that a(x) satisfies some condition, we show that there existsλ₀ > 0 such that (*) admits at least one solutions for allλ∈(0,λ₀).