Abstract
Abstract In this paper, we firstly explore the existence of solutions to the following linear Schrödinger Kirchhoff Poisson equation with critical exponential growth on the full space □3 by using the discontinuous finite element (DG) as well as the principle of centralized compactness: { − ( a + b ∫ □ 3 | ∇ u | 2 ) Δ u + V ( x ) u + φ u - 1 2 u Δ ( u 2 ) = K ( x ) u p − 2 u , x ∈ □ 3 − Δ φ = u 2 , x ∈ □ 3 \left\{ {\matrix{{ - \left( {a + b\int_{{\square^3}} {{{\left| {\nabla u} \right|}^2}} } \right)\Delta u + V\left( x \right)u + \phi u - {1 \over 2}u\Delta \left( {{u^2}} \right) = K\left( x \right){u^{p - 2}}u,} & {x \in {\square^3}} \cr { - \Delta \phi = {u^2},} & {x \in {\square^3}} \cr } } \right. , x ∈. Secondly, we make reasonable assumptions on the V, K , f functions of the equation, and use the principle of variational division to firstly obtain the corresponding energy generalization of this equation, and then we prove the corresponding generalizations of the equation satisfy the (C) c conditions. Finally, the existence of the solution of the equation is obtained by numerical simulation and then by using the Yamaji Lemma. The results show that the error of the finite element solution of the linear Schrödinger Kirchhoff Poisson equation in the spatial direction P1 reaches the optimal estimation under the L 2 -parameter in an intermittent finite element numerical simulation environment, i.e., it is proved that there exist at least 1 and 3 positive solutions to the problem. The paper achieves rich research results which are informative for the solution of this class of linear differential equations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.