Entire solutions of semilinear elliptic equations
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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.
CitationGladkov, A., & Slepchenkov, N. (2004). Entire solutions of semilinear elliptic equations. Electronic Journal of Differential Equations, 2004(86), pp. 1-10.
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