On the Best Constant for a Weighted Sobolev‐Hardy Inequality
@article{Chou1993OnTB, title={On the Best Constant for a Weighted Sobolev‐Hardy Inequality}, author={Kai-Seng Chou and Chiu Wing Chu}, journal={Journal of The London Mathematical Society-second Series}, year={1993}, volume={48}, pages={137-151} }
241 Citations
Electronic Journal of Qualitative Theory of Differential Equations
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We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear…
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Let 0 ≤ a 0. Equation (0.1) is arising from the celebrated Caffarelli-Kohn-Nirenberg inequality. For a = b < 0 and p = 2N N−2 , we show there is no positive solution of the equation (0.2) …
On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions †
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- 2001
Consider the following inequalities due to Caffarelli, Kohn, and Nirenberg [6]
where, for N ≥ 3, −∞ < a < (N − 2)/2, a ≤ b ≤ a + 1, and p = 2N/(N − 2 + 2(b − a)). We shall answer some…
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Abstract In this paper, we study negative classical solutions and stable solutions of the following k-Hessian equation $$F_k(D^2V) = (-V)^p\quad {\rm in}\;\; R^n$$with radial structure, where n ⩾ 3,…
Existence of Extremal Functions for Higher-Order Caffarelli–Kohn–Nirenberg Inequalities
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Abstract Though there has been an extensive study on first-order Caffarelli–Kohn–Nirenberg inequalities, not much is known for the existence of extremal functions for higher-order ones. The…
Sign-changing solutions for critical equations with Hardy potential
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We consider the following perturbed critical Dirichlet problem involving the Hardy-Schrodinger operator on a smooth bounded domain $\Omega \subset \mathbb{R}^N$, $N\geq 3$, with $0 \in \Omega$: $$…