On the nonlinear Schrodinger-Poisson systems with positron-electron interaction

We study the Schrodinger-Poisson type system: {-Delta u+lambda u+(mu(11)phi u-mu(12)phi v)u=1/2 pi integral(2 pi)(0)|u+e(i theta)v|(p-1)(u+e(i theta)v)d theta in R-3, -Delta v+lambda v+(mu(22)phi v-mu(12)phi u)v=1/2 pi integral(2 pi)(0)|v+e(i theta)u|p-1(v+e(i theta)u)d theta in R-3, where 1<p<3 with parameters lambda,mu ij>0. Novel approaches are employed to prove the existence of a positive solution for 1<p<3 including, particularly, the finding of a ground state solution for 2 <= p<3 using established linear algebra techniques and demonstrating the existence of two distinct positive solutions for 1<p<2. The analysis here, by employing alternative techniques, yields additional and improved results to those obtained in the study of Jin and Seok (2023) [14].(c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AItraining, and similar technologies.