We consider the following quasilinear Schrödinger system in RN\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb{R}^N}$$\end{document} with N≥3\documentclass[12pt]{minimal}
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\begin{document}$${N\geq3}$$\end{document}:
P∑i,j=1NDj(aij(u)Diu)-12∑i,j=1NDsaij(u)DiuDju-A(x)u+Fu(u,v)=0∑i,j=1NDj(aij(v)Div)-12∑i,j=1NDsaij(v)DivDjv-B(x)v+Fv(u,v)=0,\documentclass[12pt]{minimal}
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\begin{document}$$\left\{\begin{array}{l}\sum_{i,j=1}^{N}D_j(a_{ij}(u)D_i u)-\frac{1}{2}
\sum_{i,j=1}^{N}D_s a_{ij}(u) D_i u D_j u-A(x) u+F_u(u,v)=0 \\ \sum_{i,j=1}^{N}D_j(a_{ij}(v)D_iv)-\frac{1}{2}
\sum_{i,j=1}^{N}D_s a_{ij}(v) D_i v D_j v-B(x)v+F_v(u,v)=0,\end{array}
\right.$$\end{document}where Di=∂∂xi,Dsaij(s)=ddsaij(s)\documentclass[12pt]{minimal}
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\begin{document}$${D_i=\frac{\partial}{\partial x_i},\ \ D_s a_{ij}(s)=\frac{d}{ds}a_{ij}(s)}$$\end{document}, F(u,v)\documentclass[12pt]{minimal}
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\begin{document}$${F(u,v)}$$\end{document} is the coupling term, A(x)\documentclass[12pt]{minimal}
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\begin{document}$${A(x)}$$\end{document} and B(x)\documentclass[12pt]{minimal}
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\begin{document}$${B(x)}$$\end{document} are finite and sign-changing potential functions. Using an approximation scheme and q\documentclass[12pt]{minimal}
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\begin{document}$${q}$$\end{document}-Laplacian regularization, we prove the existence of infinitely many solutions for system (P)\documentclass[12pt]{minimal}
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\begin{document}$${(P)}$$\end{document}.
