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- Title
PROPERTIES OF THE LEAST ACTION LEVEL AND THE EXISTENCE OF GROUND STATE SOLUTION TO FRACTIONAL ELLIPTIC EQUATION WITH HARMONIC POTENTIAL.
- Authors
Torres Ledesma, César E.; Gutierrez, Hernán C.; Rodríguez, Jesús A.; Bonilla, Manuel M.
- Abstract
In this article we consider the following fractional semilinear elliptic equation (-Δ)s u + |x|² u = ωu + |u|²σ in RN, where s ∈ (0, 1), N > 2s, σ ∈ (0, 2s/N-2s) and ω ∈ (0, λ1). By using variational methods we show the existence of a symmetric decreasing ground state solution of this equation. Moreover, we study some continuity and differentiability properties of the ground state level. Finally, we consider a bifurcation type result.
- Subjects
ELLIPTIC equations; SEMILINEAR elliptic equations; SOBOLEV spaces; EQUATIONS of state; HARMONIC maps
- Publication
Opuscula Mathematica, 2024, Vol 44, Issue 5, p749
- ISSN
1232-9274
- Publication type
Article
- DOI
10.7494/OpMath.2024.44.5.749