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This paper is concerned with the quasilinear Schr\"{o}dinger system \begin{equation}\label{0.1} \left\{ \begin{aligned} &-\Delta u+a(x)u-\Delta(u^2)u=F_u(u,v)+h(x) \quad \; x\in \mathbb{R}^N,\\ &-\Delta v+b(x)v-\Delta(v^2)v=F_v(u,v)+g(x) \quad \; x\in \mathbb{R}^N, \end{aligned} \right. \end{equation} where $ N \geq 3$. The potential functions $a(x), b(x)\in L^\infty(\mathbb{R}^N)$ are bounded in $\mathbb{R}^N$. By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (\ref{0.1}).
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참고문헌 (17)
참고문헌 신청
C. O. Alves / 2013 / Existence of solutions for a class of nonlinear Schr¨odinger equations with potential vanishing at infinity / J. Differential Equations 254(4):1977~1991
A. Ambrosetti / 1973 / Dual variational methods in critical point theory and applications / J. Funct. Anal 14:349~381
H. Brezis / 1983 / A relation between pointwise convergence of functions and convergence of functionals / Proc. Amer. Math. Soc 88(3):486~490
C. S. Chen / 2015 / Multiple solutions for a class of quasilinear Schrodinger equations in RN / J. Math. Phys 56(7):14
C. S. Chen / 2013 / Multiple solutions to the nonhomogeneous p-Kirchhoff elliptic equation with concave-convex nonlinearities / Appl. Math. Lett 26(7):754~759
A. Ambrosetti / 1973 / Dual variational methods in critical point theory and applications / J. Funct. Anal 14:349~381
H. Brezis / 1983 / A relation between pointwise convergence of functions and convergence of functionals / Proc. Amer. Math. Soc 88(3):486~490
C. S. Chen / 2015 / Multiple solutions for a class of quasilinear Schrodinger equations in RN / J. Math. Phys 56(7):14
C. S. Chen / 2013 / Multiple solutions to the nonhomogeneous p-Kirchhoff elliptic equation with concave-convex nonlinearities / Appl. Math. Lett 26(7):754~759
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