Existence and concentration of ground state solution to a nonlocal Schrödinger equation
We study a class of Schrödinger-Kirchhoff system involving critical exponent. We aim to find suitable conditions to assure the existence of a positive ground state solution of Nehari-Pohouzaev type $u_{\varepsilon}$ with exponential decay at infinity for $\varepsilon$ and $ u_{\varepsilon}$ concentrates around a global minimum point of $ V$ as $ \varepsilon\rightarrow0^{+}.$ The nonlinear term includes the nonlinearity $f(u)\sim|u|^{p-1}u$ for the well-studied case $ p\in[3,5)$, and the less-studied case $p\in(2,3)$.
math.AP↗