Další formáty:
BibTeX
LaTeX
RIS
@article{1800680,
author = {Bhakta, Mousomi and Mukherjee, Debangana and Nguyen, Phuoc Tai},
article_number = {December},
doi = {http://dx.doi.org/10.1016/j.jde.2021.09.037},
keywords = {Hardy potential; Measure data; Linking theorem; Minimal solution; Mountain pass solution; Lane-Emden equations},
language = {eng},
issn = {0022-0396},
journal = {Journal of Differential Equations},
title = {Multiplicity and uniqueness for Lane-Emden equations and systems with Hardy potential and measure data},
url = {https://doi.org/10.1016/j.jde.2021.09.037},
volume = {304},
year = {2021}
}
TY - JOUR
ID - 1800680
AU - Bhakta, Mousomi - Mukherjee, Debangana - Nguyen, Phuoc Tai
PY - 2021
TI - Multiplicity and uniqueness for Lane-Emden equations and systems with Hardy potential and measure data
JF - Journal of Differential Equations
VL - 304
IS - December
SP - 29-72
EP - 29-72
PB - Elsevier Inc.
SN - 00220396
KW - Hardy potential
KW - Measure data
KW - Linking theorem
KW - Minimal solution
KW - Mountain pass solution
KW - Lane-Emden equations
UR - https://doi.org/10.1016/j.jde.2021.09.037
N2 - Let Omega be a C-2 bounded domain in R-N (N >= 3), delta(x) = dist(x, partial derivative Omega) and C-H(Omega) be the best constant in the Hardy inequality with respect to Q. We investigate positive solutions to a boundary value problem for Lane-Emden equations with Hardy potential of the form -Delta u - mu/delta(2) u = u(p) in Omega, u = rho nu on partial derivative Omega, (P-rho) where 0 < mu < C-H (Q), rho is a positive parameter, nu is a positive Radon measure on partial derivative Omega with norm 1 and 1 < p < N-mu, with N-mu being a critical exponent depending on N and mu. It is known from [22] that there exists a threshold value rho* such that problem (P-rho) admits a positive solution if 0 < rho <= rho*, and no positive solution if rho > rho*. In this paper, we go further in the study of the solution set of (P-rho). We show that the problem admits at least two positive solutions if 0 < rho < rho* and a unique positive solution if rho= rho*. We also prove the existence of at least two positive solutions for Lane-Emden systems {- Delta u - mu/delta(2) u = v(p) in Omega, - Delta v - mu/delta(2) v = u(q) in Omega, u = rho nu, v = sigma tau on Omega, under the smallness condition on the positive parameters rho and sigma.
ER -
BHAKTA, Mousomi, Debangana MUKHERJEE a Phuoc Tai NGUYEN. Multiplicity and uniqueness for Lane-Emden equations and systems with Hardy potential and measure data. \textit{Journal of Differential Equations}. Elsevier Inc., 2021, roč.~304, December, s.~29-72. ISSN~0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2021.09.037.
|
