Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations

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A class of semilinear elliptic differential equations was investigated in this study. By constructing the inverse function, using the method of upper and lower solutions and the principle of comparison, the existence of the maximum positive solution and the minimum positive solution was explored. Furthermore, the uniqueness of the positive solution and its asymptotic estimation at the origin were evaluated. The results show that the asymptotic estimation is similar to that of the corresponding boundary blowup problems. Compared with the conclusions of Wei’s work in 2017, the asymptotic behavior of the solution only depends on the asymptotic behavior of b(x) at the origin and the asymptotic behavior of g at infinity.