Abstract This paper is dedicated to studying the following Kirchhoff-type problem: $$ \textstyle\begin{cases} -m ( \Vert \nabla u ^{2}_{L^{2}(\mathbb{R} ^{N})} )\Delta u+V(x)u=f(u), &amp; x\in \mathbb{R} ^{N}; \\ u\in H^{1}(\mathbb{R} ^{N}), \end{cases} { ? <mm...

Abstract In this paper, we study the following coupled Choquard system in : where and , which denotes if . The function is a Riesz potential. By using Nehari manifold method, obtain existence of positive ground state solution case bounded potential periodic potential, respectively. particular, nonlinear term includes well‐studied less‐studied Moreover, it seems to be first result for

Non-homogeneous gauge ground state solutions in a six-dimensional gauge model in the presence of non-zero extended fermionic charge density fluctuations are reviewed and fully reinterpreted.

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut+∆u = ±|u|4/du for large spherically symmetric Lx(R d) initial data in dimensions d ≥ 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solutio...

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flatband Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerate with the all-spin-up and all-spin-down states. This property ...

Hard combinatorial optimization problems deal with the search for the minimum cost solutions (ground states) of discrete systems under strong constraints. A transformation of state variables may enhance computational tractability. It has been argued that these state encodings are to be chosen invertible to retain the original size of the state space. Here we show how redundant non-invertible en...

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flatband Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerated with the all-spin-up and all-spin-down states. This property...