Entire solutions of semilinear elliptic equations
Southwest Texas State University, Department of Mathematics
We consider existence of entire solutions of a semilinear elliptic equation ∆u = k(x) ƒ(u) for x ∈ ℝn, n ≥ 3. Conditions of the existence of entire solutions have been obtained by different authors. We prove a certain optimality of these results and new sufficient conditions for the nonexistence of entire solutions.
Semilinear elliptic equation, Entire solutions, Nonexistence
Gladkov, A., & Slepchenkov, N. (2004). Entire solutions of semilinear elliptic equations. <i>Electronic Journal of Differential Equations, 2004</i>(86), pp. 1-10.