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Finite Morse Index Solutions of the Fractional Henon-Lane-Emden Equation with Hardy Potential
- Kim, Soojung;
- Lee, Youngae
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1초록
In this paper, we study the fractional Henon-Lane-Emden equation associated with Hardy potential (-Delta)(s)u-gamma vertical bar x vertical bar(-2s) u=vertical bar x vertical bar(a)vertical bar u vertical bar(p-1)u in R-n. Extending the celebrated result of [14], we obtain a classification result on finite Morse index solutions to the fractional elliptic equation above with Hardy potential. In particular, a critical exponent p of Joseph-Lundgren type is derived in the supercritical case studying a Liouville type result for the s-harmonic extension problem.
키워드
finite Morse index solution; fractional Henon-Lane-Emden equations; Hardy potential; monotonicity formula; WEIGHTED NORM INEQUALITIES; STABLE-SOLUTIONS; ELLIPTIC-EQUATIONS; PARTIAL REGULARITY; DIRICHLET PROBLEM; DELTA-U; CLASSIFICATION; ASYMPTOTICS; E(U)
- 제목
- Finite Morse Index Solutions of the Fractional Henon-Lane-Emden Equation with Hardy Potential
- 저자
- Kim, Soojung; Lee, Youngae
- 발행일
- 2022-04
- 유형
- Article
- 권
- 26
- 호
- 2
- 페이지
- 251 ~ 283