Existence of semiclassical ground state solutions for a generalized Choquard equation
Abstract
In this paper, we study a generalized quasilinear Choquard equation ε^{p}∆_{p}u+V(x)u=ε<mml:mo stretchy="true" maxsize="5.2ex" minsize="5.2ex">(</mml:mo>∫R^{N} <mml:mfrac>Q(y)F(u(y))</mml:mfrac><mml:mo stretchy="true" maxsize="5.2ex" minsize="5.2ex">)</mml:mo>Q(x)f(u) in R^{N}, where ∆_{p} is the pLaplacian operator, 1<p<N, V and Q are two continuous real functions on R^{N}, 0<μ<N, F(s) is the primate function of f(s) and ε is a positive parameter. Under suitable assumptions on p,μ and f, we establish a new concentration behavior of solutions for the quasilinear Choquard equation by variational methods. The results are also new for the semilinear case p=2.
 Publication:

Journal of Differential Equations
 Pub Date:
 December 2014
 DOI:
 10.1016/j.jde.2014.08.004
 Bibcode:
 2014JDE...257.4133A