The kernel space of linear operator for a class of Grushin equation
DOI:
https://doi.org/10.12775/TMNA.2025.017Słowa kluczowe
Kernel space, linear operator, Grushin equationAbstrakt
In this paper, we concern the kernel of linear operator for a class of Grushin equation. First, we study the kernel space of linear operator for a general Grushin equation. Then, we provide an exact expression for the kernel space of linear operator associated with a special Grushin equation. Finally, we prove the linear operator related to the singularly perturbed Grushin equation is invertible when restricted to the complement of its approximate kernel space.Bibliografia
C.O. Alves and A.R.F. de Holanda, A Berestycki–Lions type result for a class of degenerate elliptic problems involving the Grushin operator, Proc. Roy. Soc. Edinburgh 153 (2023), no. 4, 1244–1271.
W. Bauer, K. Furutani and C. Iwasaki, Fundamental solution of a higher step Grushin type operator, Adv. Math. 271 (2015), 188–234.
W. Bauer, Y. Wei and X. Zhou, A priori estimates and moving plane method for a class of Grushin equation, Arxiv: 2412.08039v1.
D.M. Cao, S.J. Peng and S.S. Yan, Singularity Perturbed Methods for Nonlinear Elliptic Problems, Cambridge University Press, 2021.
B. Gidas, W.M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243.
M. Grossi, On the number of single-peak solutions of the nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire. 19 (2002), no. 3, 261–280.
Y. Guo, S. Peng and S. Yan, Local uniqueness and periodicity induced by concentration, Proc. London Math. Soc. 114 (2017), no. 6, 1005–1043.
L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 141–171.
Q.Q. Hua, C.H. Wang and J. Yang, Existence and local uniqueness of multi-peak solutions for the Chern–Simons–Schrödinger system, Arxiv: 2210.17427.2022.
M.K. Kwong, Uniqueness of positive solutions of ∆u − u + up = 0 in Rn , Arch. Rational Mech. Anal. 105 (1989), 243–266.
M. Liu, Z.W. Tang and C.H. Wang, Infinitely many solutions for a critical Grushin-type problem via local Pohozaev identities, Ann. Mat. Pura Appl. 199 (2020), 1737–1762.
P. Luo, S. Peng and C. Wang, Uniqueness of positive solutions with concentration for the Schrödinger–Newton problem, Calc. Var. Partial Differential Equations 59 (2020), no. 2, 60.
P.H. Rabinowitz, Multiple critical points of perturbed symmetric functionals, Trans. Amer. Math. Soc. 272 (1982), no. 2, 753–769.
P. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43 (1992), no. 2, 270–291.
N.M. Tri, Superlinear equations for degenerate elliptic operators, preprint ICTP, World Sci. Publ., Teaneck, N.J., 1995 , 1–17.
N.M. Tri, On the Grushin equation, Mat. Zametki 63 (1998), no. 1, 95–105.
X. Wang, On the concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys. 153 (1993), 229–244.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Licencja
Prawa autorskie (c) 2025 Yawei Wei, Xiaodong Zhou
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
Statystyki
Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0
