Generalized coherent states for relativistic model of a linear oscillator

Infinitely many subharmonic solutions for nonlinear equations with singular $ \phi $-Laplacian

“…However, there are few results on the multiplicity of subharmonic solutions of Eq. (1). Recently, Boscaggin, Garrione and Feltrin, Fonda and Toader, Donde and Zanolin applied the Poincaré-Birkhoff twist theorem to discuss related problems, see [8,7,19,14].…”

“…Subharmonic mechanical vibrations of nonlinear systems under relativistic effect. Relativistic oscillator models for particle motions are a subject of rather broad interest nowadays, which have been widely used in different branches of theoretical physics such as quantum mechanics, statistical mechanics, superconductivity theory, nuclear physics, and so forth [21,27,1].…”

“…Introduction. In this paper we deal with the existence and multiplicity of subharmonic solutions of nonlinear second order equation (φ(x )) + g(t, x) = 0 (1) involving the singular φ-Laplacian, where φ : (−a, a) → R is an increasing homeomorphism with φ(0) = 0, and g : R × R → R is a continuous and periodic function with period 2π with respect to time t. Also, we assume that, there are constants ε 0 > 0 and d 0 > 0, such that g(t, x) satisfies the following sign condition:…”

Nonlinear systems with singular vectorϕ-Laplacian under the Hartman-type condition

“…Such problems arise from the relativistic oscillator models and curvature operator equations [1]. For example, the special relativity operator φ : B(1) → R N is given by…”

Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials

“…The Pollaczek polynomials were involved in the description [47] of the wave functions of relativistic model of linear harmonic oscillator in the frame-work of the quasi-potential approach. (For more details on this model and its variants we refer the reader to [48]- [51]). …”