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Least energy sign-changing solutions for super-quadratic Schr\"{o}dinger-Poisson systems in R^3
Sofiane Khoutir
Keywords:35J20; 35J60
Abstract:
      In this paper we study the following Schr?dinger-Poisson systems -?u+Vu+λφ(x)u=f(u), in R^3, -Δφ=u^2, in R^3, Where V,λ>0 and f∈C(R). Under more relaxed assumptions on f, using variational methods in combination with the Pohozaev identity, we prove that the above problem possesses a least energy sign-changing solution and a ground state solution provided that λ is sufficiently small. Moreover, we prove that the energy of a sign-changing solution is strictly larger than that of the ground state solutions. Our results generalize and improve some recent results in the literature.