Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equation on Rn

Soohyun Bae; Wei Ming Ni

doi:10.1007/PL00004468

Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equation on Rⁿ

Soohyun Bae, Wei Ming Ni

School of Mathematics

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

The existence/nonexistence question is studied for the inhomogeneous elliptic equation Δu + u^p + μf(x) = 0 in Rⁿ. In particular, we establish that the above equation possesses infinitely many positive entire solutions for small μ > 0 provided that n ≥ 11, p is large enough, and the locally Hölder continuous function f satisfies suitable decay conditions at ∞.

Original language	English (US)
Pages (from-to)	191-210
Number of pages	20
Journal	Mathematische Annalen
Volume	320
Issue number	1
DOIs	https://doi.org/10.1007/PL00004468
State	Published - 2001

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abstract = "The existence/nonexistence question is studied for the inhomogeneous elliptic equation Δu + up + μf(x) = 0 in Rn. In particular, we establish that the above equation possesses infinitely many positive entire solutions for small μ > 0 provided that n ≥ 11, p is large enough, and the locally H{\"o}lder continuous function f satisfies suitable decay conditions at ∞.",

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AB - The existence/nonexistence question is studied for the inhomogeneous elliptic equation Δu + up + μf(x) = 0 in Rn. In particular, we establish that the above equation possesses infinitely many positive entire solutions for small μ > 0 provided that n ≥ 11, p is large enough, and the locally Hölder continuous function f satisfies suitable decay conditions at ∞.

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Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equation on Rⁿ

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