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@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.
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