The asymptotic behaviour of the ground state solutions for Hénon equation

By Daomin Cao, Shuangjie Peng. 2003

133 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d84ae58a38c72a754597bdc240317ad4209e863a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Shusen Yan
2. Shuangjie Peng
3. Jun-cheng Wei
4. D. Smets
5. Marta Calanchi
6. Thomas Bartsch
7. E. Serra
8. Bernhard Ruf

In Computational Theory and Mathematics

1. Shusen Yan
2. Shuangjie Peng
3. E. Serra
4. Marta Calanchi
5. Jun-cheng Wei
6. D. Smets
7. Michel Willem
8. M. Badiale

Citations in the corpus

• Radial and non radial solutions for Hardy–Hénon type elliptic systems (2010, background): “In a related result, Cao and Peng proved in [5] that for α > 0 and p + 1 sufficiently close to 2∗ the ground-state solutions of (2) are not radial since they possess a unique maximum point which tends to ∂ as p + 1 → 2∗.”
• Infinitely many nonradial solutions for the Hénon equation with critical growth (2013, background): “The reader can refer to [1], [2], [4], [8], [10], [11], and [14] for results on Hénon equations involving subcritical and near critical exponents.”
• Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, background): “Moreover, some interesting results such as the existence and non-existence of the extremal functions and the symmetry and non-symmetry of the extremal functions were discussed; see [3, 9, 16, 28, 30, 34, 35], for instance.”
• Non radial positive solutions for the Hénon equation with critical growth (2005, background): “Further results on partial symmetry and asymptotic behavior of ground states as p→ 2∗ or as α→∞ can be found in [11] and [5].”
• Partial symmetry and asymptotic behavior for some elliptic variational problems (2003, methodology): “2 U ( x−y e ). Theorem (Cao and Peng [ 9 ]). Let N ≥ 3 and α> 0. If (up) is a sequence of ground state solutions of (3) with p → 2 ∗ , then up to a subsequence there exists x0 ∈ ∂Ω such that – |∇up| 2 → µδx0 in the sense of measure Partial symmetry 63”
• Multiplicity Results for the Supercritical Hénon Equation (2004, background): “Further results on the subcritical Hénon equation (such as symmetry properties of solutions and blow–up profile of ground states) can be found in [1], [3] and [10].”