The Existence of Ground‐State Solutions for Critical HéNon Equations in ℝNRN

In this paper we confirm that with is exactly the critical exponent for the embedding from into () (see [3, 4]) and name it as the upper Hénon‐Sobolev critical exponent. Based on this fact, we study the ground‐state solutions of critical Hénon equations in via the Nehari manifold methods and the great idea of Brézis‐Nirenberg in [9]. We establish the existence of the positive radial ground‐state solutions for the problem with one single upper Hénon‐Sobolev critical exponent. We also deal with the existence of the nonnegative radial ground‐state solutions for the problems with multiple critical exponents, including Hardy‐Sobolev critical exponents or Sobolev critical exponents or the upper Hénon‐Sobolev critical exponents.