On the stability of the positive radial steady states for a semilinear Cauchy problem

Abstract

This paper is contributed to the Cauchy problem

On the stability of the positive steady states for a nonhomogeneous semilinear Cauchy problem

“…Extending the earlier results by Fujita in [10], Weissler in [25], Lee and Ni in [16], Wang in [24], Gui, Ni and Wang [13,16] and Deng, Li and Liu in [9], we will prove for general f (x) which satisfies (f.1)-(f.3), Theorem 1.2.…”

“…Under the topology introduced in (1.8), Deng, Li and Liu extended the result to a more general class of K(x) in [9]. The second purpose of this paper is to discuss the stability of the positive steady states of (1.2) with nonzero f (x) by constructing super-and subsolutions.…”

On the semistability of the minimal positive steady state for a nonhomogeneous semilinear Cauchy problem

“…for some positive integer Λ > 1, where a i , b j and c 1 are similar to (3.18) of [7]. Proposition 2.2.…”

ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS IN ℝn

“…Please refer to [16,18,20,21,23] and the references therein. There have been many works devoted to studying the existence of positive solutions of (1.3) in R n after the first contribution by Ni [20] in 1982, see [2,6,7,8,11,12,23] and the references therein. One of the features of the equation is that (1.3) can posses infinitely many solutions as long as the exponent p and the dimension n are large enough.…”