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This paper is concerned with the following Kirchhoff-Schr\"{o}d\-inger-Poisson system $$ \scalebox{0.84}{$\displaystyle\left\{\!\! \begin{array}{ll} \displaystyle -\big(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\mathrm{d}x\big)\Delta u + V(x)u+\mu\phi u=\lambda f(x)|u|^{p-2}u+g(x)|u|^{q-2}u, &\mbox{ in }\mathbb{R}^{3},\\ -\Delta \phi= \mu |u|^{2}, &\mbox{ in }\mathbb{R}^{3},\\ \end{array} \right.$} $$ where $a>0,~b,~\mu\geq0$, $p\in(1,2)$, $q\in[4,6)$ and $\lambda>0$ is a parameter. Under some suitable assumptions on $V(x)$, $f(x)$ and $g(x)$, we prove that the above system has at least two different nontrivial solutions via the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Some recent results from the literature are improved and extended.
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참고문헌 (38)
참고문헌 신청
C. O. Alves / 2005 / Positive solutions for a quasilinear elliptic equation of Kirchhotype / Comput. Math. Appl. 49(1):85~93
A. Ambrosetti / 1973 / Dual variational methods in critical point theory and applications / J. Funct. Anal 14:349~381
A. Arosio / 1996 / On the well-posedness of the Kirchhostring / Trans. Amer. Math. Soc 348(1):305~330
A. Azzollini / 2008 / Ground state solutions for the nonlinear Schrodinger-Maxwell equations / J. Math. Anal. Appl 345(1):90~108
T. Bartsch / 1995 / Existence and multiplicity results for some superlinear elliptic problems on RN / Comm. Partial Dierential Equations 20(9-10):1725~1741
A. Ambrosetti / 1973 / Dual variational methods in critical point theory and applications / J. Funct. Anal 14:349~381
A. Arosio / 1996 / On the well-posedness of the Kirchhostring / Trans. Amer. Math. Soc 348(1):305~330
A. Azzollini / 2008 / Ground state solutions for the nonlinear Schrodinger-Maxwell equations / J. Math. Anal. Appl 345(1):90~108
T. Bartsch / 1995 / Existence and multiplicity results for some superlinear elliptic problems on RN / Comm. Partial Dierential Equations 20(9-10):1725~1741
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