Schrödinger–Poisson system with steep potential well

Existence and concentration of solutions for the nonlinear Kirchhoff type equations with steep well potential

The existence of nontrivial solution for a class of sublinear biharmonic equations with steep potential well

where 2u = ( u), N > 4, λ > 0, 1 < q < 2 and μ ∈ [0,μ0], 0 < μ0 <∞. The continuous function f verifies the assumptions: (f1) f (s) = o(|s|) as s→ 0; (f2) f (s) = o(|s|) as |s| →∞; (f3) F(u0) > 0 for some u0 > 0, where F(u) = ∫ u 0 f (t) dt. According to hypotheses (f1)–(f3), the number cf = max s =0 | f (s) s | > 0 is well defined (see [1]). The continuous functions α and K verify the assumptio...

Potential problems with "well fitting" models.

The assessment of model fit is a more complex and indeterminate process than is commonly acknowledged by researchers who use structural equation modeling (SEM) techniques. Even models that are well fitting according to commonly used statistical tests and descriptive fit indices can have significant problems and ambiguities. The authors discuss 7 potential difficulties that can arise and that sh...

Berry phase for a particle in an infinite spherical potential well with moving wall

In this paper we calculate the Berry phase for a wave function of a particle in an infinite spherical potential well with adiabatically varying. In order to do this, we need the solutions of the corresponding Schrödinger equation with a time dependent Hamiltonian. Here, we obtain these solutions for the first time. In addition, we calculate the Berry phase in one dimensional case for an infinit...

Sign-changing Multi-bump Solutions for Nonlinear Schrödinger Equations with Steep Potential Wells

We study the nonlinear Schrödinger equations: (Pλ) −∆u+(λa(x)+1)u = |u|p−1u, u ∈ H(R ), where p > 1 is a subcritical exponent, a(x) is a continuous function satisfying a(x) ≥ 0, 0 < lim inf |x|→∞ a(x) ≤ lim sup|x|→∞ a(x) < ∞ and a−1(0) consists of 2 connected bounded smooth components Ω1 and Ω2. We study the existence of solutions (uλ) of (Pλ) which converge to 0 in RN \ (Ω1 ∪Ω2) and to a presc...