We are concerned with the multiplicity of positive solutions for singular superlinear and subcritical Schrödinger equation [Formula: see text] beyond Nehari extremal value, as defined in [Y. Il’yasov, On extreme values manifold via nonlinear Rayleigh’s quotient, Topol. Methods Nonlinear Anal. 49 (2017) 683–714], when potential may change its sign, text], is a continuous function, real parameter...

Abstract We compare ground states for the nonlinear Schrödinger equation on metric graphs, defined as global minimizers of action functional constrained Nehari manifold, and least solutions, namely among all solutions to equation. In principle, four alternative cases may take place: do exist (thus coinciding with solutions); not while do; both levels two minimizing problems coincide; are differ...

This paper is concerned with the following nonlinear Chern-Simons-Schrödinger equation zero mass potential $ \begin{align} -\Delta u+\lambda\left(\frac{h_u^2(|x|)}{|x|^2}+\int^{\infty}_{|x|}\frac{h_u(s)}{s}u^2(s)ds\right)u = -a|u|^{p-2}u+f(u),\ \ x\in\mathbb{R}^2, \end{align} where a, \lambda>0 $, p\in (2,3) and$ h_u(s) \int^s_0\frac{\tau}{2}u^2(\tau)d\tau \frac{1}{4\pi}\int_{B_s}u^2(x)dx $i...

has been studied extensively by many researchers, where 2 < p < 6. This system has been first introduced in [5] as a physical model describing a charged wave interacting with its own electrostatic field in quantum mechanic. The unknowns u and Φ represent the wave functions associated to the particle and electric potential, and functions V and K are respectively an external potential and nonnega...

and Applied Analysis 3 In this paper, we also consider themultiplicity of solutions of (7). For each l ∈ Z, let l ∗ u = (u n+lT ) n∈Z , ∀u = (u n ) n∈Z , (21) which defines a Z-action on E. By the periodicity of the coefficients, we know that both J and J󸀠 are Z-invariants. Therefore, ifu ∈ E is a critical point of J, so is l∗u. Two critical points u 1 , u 2 ∈ E of J are said to be geometricall...

and Applied Analysis 3 DNLS equation is one of the most important inherently discrete models, which models many phenomena in various areas of applications see 2–4 and reference therein . For example, in nonlinear optics, DNLS equation appears as a model of infinite wave guide arrays. In the past decade, the existence and properties of mobile discrete solitons/breathers in DNLS equations have be...