Soliton Solutions for Quasilinear Schrödinger Equations Involving Convolution and Critical Nonlinearities
Tóm tắt
In this paper, we establish the existence, multiplicity and concentration behaviour of positive solutions for quasilinear Schrödinger equations with Choquard term and critical nonlinearities:
$$\begin{aligned} -\varepsilon ^{p}(\Delta _p u+u\Delta _p(u^2))+ V(x)|u|^{p-2}u = \varepsilon ^{\mu -N}\left( |x|^{-\mu }*F(u)\right) f(u) + |u|^{2p^*-2}u, \end{aligned}$$
where
$$\varepsilon >0$$
is a parameter,
$$0<\mu
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