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Zbl 1189.35081
Li, Qingdong; Su, Han; Wei, Zhongli
Existence of infinitely many large solutions for the nonlinear Schrödinger-Maxwell equations. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 11, 4264-4270 (2010). ISSN 0362-546X

Summary: We study the nonlinear stationary Schrödinger-Maxwell equations $$\cases -\Delta u+V(x)u+ \varphi u=f(x,u) &\text{in }\Bbb R^3,\\ -\Delta\varphi= u^2 &\text{in }\Bbb R^3. \endcases \tag $*$ $$ Using the variant fountain theorem introduced by {\it W. Zou} [Manuscr. Math. 104, No.~3, 343--358 (2001; Zbl 0976.35026)], under certain assumptions on $V$ and $f$, we get infinitely many large solutions for $(*)$.

MSC 2000:: *35J47
35J50 Systems of elliptic equations, variational methods
35Q40 PDE from quantum mechanics
35B40 Asymptotic behavior of solutions of PDE

Keywords: Schrödinger-Maxwell equations; variational methods; variant fountain theorem

Citations: Zbl 0976.35026

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