数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (1): 197-208.doi: 10.1016/S0252-9602(12)60012-5

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BOUND STATES FOR A CLASS OF QUASILINEAR SCALAR FIELD EQUATIONS WITH POTENTIALS VANISHING AT INFINITY

Athanasios N. Lyberopoulos   

  1. Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece
  • 收稿日期:2011-10-16 出版日期:2012-01-20 发布日期:2012-01-20

BOUND STATES FOR A CLASS OF QUASILINEAR SCALAR FIELD EQUATIONS WITH POTENTIALS VANISHING AT INFINITY

Athanasios N. Lyberopoulos   

  1. Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece
  • Received:2011-10-16 Online:2012-01-20 Published:2012-01-20

摘要:

We study the existence and non-existence of bound states (i.e., solutions in W1, p (RN )) for a class of  quasilinear scalar field equations of the form

-?pu+V(x)|u| p-2u = a(x)|u| q-2u, x ∈ RN , 1 < p < N,

when the potentials V(·) 0 and a(·) decay to zero at infinity.

关键词: p-Laplacian, bound states, decaying potentials, Hardy potential, weighted Sobolev spaces

Abstract:

We study the existence and non-existence of bound states (i.e., solutions in W1, p (RN )) for a class of  quasilinear scalar field equations of the form

-?pu+V(x)|u| p-2u = a(x)|u| q-2u, x ∈ RN , 1 < p < N,

when the potentials V(·) 0 and a(·) decay to zero at infinity.

Key words: p-Laplacian, bound states, decaying potentials, Hardy potential, weighted Sobolev spaces

中图分类号: 

  • 35J92