Abstract
In this work we prove the existence of solutions for a class of generalized Choquard equations involving the Delta _Phi -Laplacian operator. Our arguments are essentially based on variational methods. One of the main difficulties in this approach is to use the Hardy–Littlewood–Sobolev inequality for nonlinearities involving N-functions. The methods developed in this paper can be extended to wide classes of nonlinear problems driven by nonhomogeneous operators.
Highlights
The stationary Choquard equation − Δu + V (x)u = RN |u|p |x − y|λ dx |u|p−2u in RN, (1.1)where N ≥ 3, 0 < λ < N, has appeared in the context of various physical models
Where N ≥ 3, 0 < λ < N, has appeared in the context of various physical models. This equation plays an important role in the theory of Bose–Einstein condensation where it accounts for the finite-range many-body interactions
[1] and Pekar [2] in relationship with the quantum theory of a polaron, where free electrons in an ionic lattice interact with phonons associated to deformations of the lattice or with the polarisation that it creates on the medium
Summary
Where N ≥ 3, 0 < λ < N , has appeared in the context of various physical models. This equation plays an important role in the theory of Bose–Einstein condensation where it accounts for the finite-range many-body interactions. Used this equation in the Hartree–Fock theory of one-component plasma. This equation was proposed by Penrose in [4] as a model of self-gravitating matter and is known in that context as the Schrodinger–Newton equation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
