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

作者：Lyberopoulos Athanasios N^*

来源：Acta Mathematica Scientia, 2012, 32(1): 197-208.

DOI：10.1016/s0252-9602(12)60012-5

• p-Laplacian
• bound states
• decaying potentials
• Hardy potential
• weighted Sobolev spaces

We study the existence and non-existence of bound states (i.e., solutions in W-1,W-P(R-N)) for a class of quasilinear scalar field equations of the form
-Delta(p)u+ V(x)vertical bar u vertical bar(p-2)u = a(x)vertical bar u vertical bar(q-2)u, x is an element of R-N, 1 < p < N,
when the potentials V(.) >= 0 and a(.) decay to zero at infinity.

• 出版日期2012-1