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In the paper, by using the variational methods we study a non-autonomous Schrödinger-Bopp-Podolsky system, where a > 0, 3 < p < 4 are fixed, λ > 0 is a parameter, and the potentials V, Q satisfy appropriate assumptions. We give some existence results, depending on the parameter λ. Moreover the results are still valid for the classical Schrödinger-Poisson system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of nontrivial solution for the following class of Choquard equation where N ∈ N , N ≥ 3 , α ∈ (0 , N) , I α is a Riesz potential, λ > 0 is a parameter, p = N + α N - 2 is the upper Hardy–Littlewood–Sobolev critical exponent and q ∈ (2 , 2 N N - 2). We prove that there exists λ 0 > 0 such that for λ ≥ λ 0 , problem (1) possesses one positive radial solution. [ABSTRACT FROM AUTHOR]

We consider the existence of positive solutions to the following Kirchhoff type equation with critical exponent −a+b∫ℝ3|∇u|2dxΔu=λV(x)u+K(x)u5,u∈D1,2(ℝ3),where a>0, b>0, and λ>0 is a parameter. Under some assumptions, two positive solutions are obtained by means of variational methods. It is worth emphasizing that for the local minimal solution, we use an entirely new method, and its some properties are also obtained. [ABSTRACT FROM AUTHOR]