Asymptotic Behaviors For Positive Solutions Of Some Semilinear Elliptic Equation △u+|x|^l₁u^p-|x|^l₂u^q=0

This thesis of Master is composed of three chapters.We mainly study the asymptotic behavior of some semilinear elliptic equations. In 1959, Kato [18] investigated the asymptotic behavior of solution of equationA series of nice results were obtained in his paper and they become very useful in the study of existence and nonexistence of solution ofLi [23], Li and Ni [24, 25, 26] have studied the equation (1) and obtained results concerning the asymptotic in equation (1). In 1992, M. K. Kwong, J. B. Mcleod, L. A. Peletier and W. C. Troy [20] have studied the equationin Rⁿ, n > 2. They discussed the existence and uniqueness of positive, radial symmetric solution the equation with q > p > (n + 2)/(n - 2).We study the asymptotic behavior of positive radial solutions of the equation (1) in Rⁿ This equation arises in various problems in applied mathematics, e.g. in the study of phase transitions, nuclear cores and more recently in population genetics. In particular, we will study the asymptotic behavior of positive radial solutions of the semilinear equationat infty, where p , q , l₁ , l₂, satisfying for some positive constants c,σ, such thatChapter 1, introduces the background of the problem-researching and the recent development of the research in this field. In chapter 2, On another conditions, we mainly study the asymptotic behavior of some semilinear elliptic equation (2), where p , q > 1 , l₁ , l₂ >-2 are constants,σ=l₁+2/p-1=l₂+2/q-1 and n-2-2σ≠0. and we obtain some results.In chapter 3, we mainly study the asymptotic behavior of some semilinear elliptic equation (2), where p , q , l₁ ,l₂ are constants, and we obtain some results.