Semilinear Elliptic Equations Involving Concave-Convex Nonlinearities and Two Critical Hardy-Sobolev Exponents

Project: National Science and Technology CouncilNational Science and Technology Council Academic Grants

Project Details

Abstract

where Ω ? RN (N ? 3) is a bounded domain with smooth boundary @Ω such that the points 0; ? 2 Ω, ? > 0, 1 ? q < 2, 0 < t1; t2 < 2, ? < ¯?, ¯? = ( N 􀀀 2 2 )2 is the best Hardy constant, and all 0 < t < 2, 2?(t) = 2(N􀀀t) N􀀀2 is the critical Hardy-Sobolev exponent. Note that 2?(0) = 2? = 2N N􀀀2 is the critical Sobolev exponent. By variational methods and analysis techniques, we hope to obtain the existence and multiplicity results of positive solutions to the equation (E?).</

Project IDs

Project ID:PA10406-1336
External Project ID:MOST104-2115-M182-002
StatusFinished
Effective start/end date01/08/1531/07/16

Keywords

  • semilinear elliptic equation
  • critical exponent
  • Hardy-Sobolev inequality

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