Abstract Non-relativistic Helium-like ions (−e, −e, Ze) with static nucleus in a d−dimensional space (d > 1) are considered. Assuming r−1Coulomb interactions, 2-parametric correlated Hylleraas-type trial function is used to calculate the ground state energy of system domain Z ≤ 10. For odd d = 3, 5, variational given by rational algebraic parameters whilst for even 2, 4 it shown first time th...

We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The corresponding BCS equations are derived and solved within the finite temperature retarded realtime Green’s functions formalism. The quasiparticle excitation spectrum is four-fold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. A two-fol...

In this paper, we study the nonlinear Schrödinger equation $$ -\Delta u+V(x)u=f(x,u) on lattice graph $$\mathbb {Z}^{N}$$ . Using Nehari method, prove that when f satisfies some growth conditions and potential function V is periodic or bounded, above admits a ground state solution. Moreover, extend our results from to quasi-transitive graphs.

We employing a minimization arguments on appropriate Nehari manifolds, we obtain ground state solutionsfor non-local elliptic system driven by the fractional a(.)-Laplacian operator, with Dirichlet boundaryconditions type.

We consider finite time blowup solutions of the L 2-critical cubic focusing nonlinear Schrödinger equation on R 2. Such functions, when in H 1 , are known to concentrate a fixed L 2-mass (the mass of the ground state) at the point of blowup. Blowup solutions from initial data that is only in L 2 are known to concentrate at least a small amount of mass. In this paper we consider the intermediate...