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math.AP2019
The Nehari manifold for indefinite Kirchhoff problem with Caffarelli-Kohn-Nirenberg type critical growth
Pawan Kumar Mishra, Joao Marcos do Ó, David G. Costa
In this paper we study the following class of nonlocal {problems} involving Caffarelli-Kohn-Nirenberg type critical growth \begin{align*} L(u)&-λh(x)|x|^{-2(1+a)}u=μf(x)|u|^{q-2}u+…
math.AP2017
Existence and concentration of positive solutions for nonlinear Kirchhoff type problems with a general critical nonlinearity
Jianjun Zhang, David G. Costa, João Marcos Do Ó
We are concerned with the following Kirchhoff type equation $$-\varepsilon^2 M \left(\varepsilon^{2-N} \int_{\mathbb{R}^N} | \nabla u|^2\, \mathrm{d} x\right) Δu+V(x)u = f(u),\ x \…
math.AP2012
Concentration profiles for the Trudinger-Moser functional are shaped like toy pyramids
Cyril Tintarev, David G. Costa
This paper answers the conjecture of Adimurthi and Struwe that the semilinear Trudinger-Moser functional (as well as functionals with more general critical nonlinearities) satisfie…