| 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. |
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