Volume 13, Issue 3
On the Radial Ground State of p-Laplacian Equation Involving Super-critical or Critical Exponents

Benjin Xuan & Zuchi Chen

J. Part. Diff. Eq., 13 (2000), pp. 193-206.

Published online: 2000-08

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  • Abstract
In this paper, we consider the existence and uniqueness of the radial ground state to the following p-Laplacian equation involving super-critical or critical exponents: Δ_pu + u^q - |Du|^σ = 0, x ∈ R^n, 2 ≤ p < n, q ≥ [n(p - 1) + p]/(n - p), σ > 0. Applying the shooting argument, the Schauder's fixed point theorem and some delicate estimates of auxiliary functions, we study the influence of the parameters n, p, q, σ on the existence and uniqueness of the radial ground state to the above p-Laplacian equation.
  • Keywords

p-Laplacian equation super-critical exponents critical exponents radial ground state shooting argument

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@Article{JPDE-13-193, author = {}, title = {On the Radial Ground State of p-Laplacian Equation Involving Super-critical or Critical Exponents}, journal = {Journal of Partial Differential Equations}, year = {2000}, volume = {13}, number = {3}, pages = {193--206}, abstract = { In this paper, we consider the existence and uniqueness of the radial ground state to the following p-Laplacian equation involving super-critical or critical exponents: Δ_pu + u^q - |Du|^σ = 0, x ∈ R^n, 2 ≤ p < n, q ≥ [n(p - 1) + p]/(n - p), σ > 0. Applying the shooting argument, the Schauder's fixed point theorem and some delicate estimates of auxiliary functions, we study the influence of the parameters n, p, q, σ on the existence and uniqueness of the radial ground state to the above p-Laplacian equation.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5506.html} }
TY - JOUR T1 - On the Radial Ground State of p-Laplacian Equation Involving Super-critical or Critical Exponents JO - Journal of Partial Differential Equations VL - 3 SP - 193 EP - 206 PY - 2000 DA - 2000/08 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5506.html KW - p-Laplacian equation KW - super-critical exponents KW - critical exponents KW - radial ground state KW - shooting argument AB - In this paper, we consider the existence and uniqueness of the radial ground state to the following p-Laplacian equation involving super-critical or critical exponents: Δ_pu + u^q - |Du|^σ = 0, x ∈ R^n, 2 ≤ p < n, q ≥ [n(p - 1) + p]/(n - p), σ > 0. Applying the shooting argument, the Schauder's fixed point theorem and some delicate estimates of auxiliary functions, we study the influence of the parameters n, p, q, σ on the existence and uniqueness of the radial ground state to the above p-Laplacian equation.
Benjin Xuan & Zuchi Chen . (2019). On the Radial Ground State of p-Laplacian Equation Involving Super-critical or Critical Exponents. Journal of Partial Differential Equations. 13 (3). 193-206. doi:
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