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In this paper, we consider the following Schr\"{o}dinger-Kirch\-hoff-type equations \[ \left[a+b\left(\int_{\mathbb{R}^{N}}(|\nabla u|^{2}+V(x)|u|^{2})dx\right)\right][-\Delta u+V(x)u]=f(x,u), ~~\mbox{in}~ \mathbb{R}^{N}. \] Under certain assumptions on $V$ and $f$, some new criteria on the existence and multiplicity of nontrivial solutions are established by the Morse theory with local linking and the genus properties in critical point theory. Some results from the previously literature are significantly extended and complemented.
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참고문헌 (25)
참고문헌 신청
C. O. Alves / 2005 / Positive solutions for a quasilinear elliptic equation of Kirchhoff type / Comput. Math. Appl 49(1):85~93
T. Bartsch / 1997 / Critical point theory for asymptotically quadratic functionals and applications to problems with resonance / Nonlinear Anal 28(3):419~441
V. Benci / 1998 / An eigenvalue problem for the Schr¨odinger-Maxwell equations / Topol. Methods Nonlinear Anal 11(2):283~293
K. Chang / 1993 / Infinite Dimensional Morse Theory and Multiple Solution Problems / Birkh¨auser
P. Chen / 2014 / Infinitely many solutions for Schr¨oginger-Maxwell equations with indefinite sign subquadratic potentials / Appl. Math. Comput 226:492~502
T. Bartsch / 1997 / Critical point theory for asymptotically quadratic functionals and applications to problems with resonance / Nonlinear Anal 28(3):419~441
V. Benci / 1998 / An eigenvalue problem for the Schr¨odinger-Maxwell equations / Topol. Methods Nonlinear Anal 11(2):283~293
K. Chang / 1993 / Infinite Dimensional Morse Theory and Multiple Solution Problems / Birkh¨auser
P. Chen / 2014 / Infinitely many solutions for Schr¨oginger-Maxwell equations with indefinite sign subquadratic potentials / Appl. Math. Comput 226:492~502
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