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Infinitely many solutions for a semilinear elliptic equation with sign-changing potential. (English) Zbl 1169.35335

Summary: We consider a similinear elliptic equation with sign-changing potential \( - \Delta u - V(x)u=f(x,u), u\in H^{1}(\mathbb R^{N})\), where \(V(x)\) is a function possibly changing sign in \(\mathbb R^{N}\). Under certain assumptions on \(f\), we prove that the equation has infinitely many solutions.

MSC:

35J60 Nonlinear elliptic equations
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References:

[1] doi:10.2307/2159436 · Zbl 0764.35031 · doi:10.2307/2159436
[2] doi:10.1007/s00526-004-0293-6 · Zbl 1078.35113 · doi:10.1007/s00526-004-0293-6
[3] doi:10.3934/dcds.2001.7.703 · Zbl 1021.35030 · doi:10.3934/dcds.2001.7.703
[6] doi:10.1007/BF02384570 · Zbl 1088.35019 · doi:10.1007/BF02384570
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