We analyze a splitting integrator for the time discretization of Schrödinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. prove that this has order convergence one in $p$th mean sense, any $p\geq1$ some Sobolev spaces. schemes preserves $L^2$-norm, which is crucial property proof strong result. Finally, numerical experiments illustrate performance proposed s...

In this paper, we first establish a criterion based on contractive function for the existence of generalized polynomial attractors. This only involves some rather weak compactness associated with repeated inferior limit and requires no compactness, which makes it suitable critical cases. Then by abstract theorem, verify attractor estimate its attractive speed wave equation nonlocal damping, ant...

We consider the Cauchy problem for generalized Fornberg–Whitham equation with dissipation. This is one of nonlinear, nonlocal and dispersive-dissipative equations. The main topic this paper an asymptotic analysis solutions to problem. prove that solution converges modified heat kernel. Moreover, we construct second term asymptotics depending on degree nonlinearity. In view those profiles, inves...

The well-known Van der Pol equation with delayed feedback is considered. It assumed that the delay factor large enough. In study of dynamics, critical cases in problem stability zero equilibrium state are identified. shown they have infinite dimension. For such cases, special local analysis methods been developed. main result construction nonlinear evolutionary boundary value problems, which pl...

We prove the existence of multiple positive solutions nonlinear second-order nonlocal boundary value problems with term having derivative dependence. allow nonlinearity to grow quadratically respect derivatives. obtain a priori bounds for norms derivatives by using recently obtained Gronwall-type inequality. Three examples illustrate some results. This article is part theme issue ‘Topological d...

We study the existence of positive solutions for a Riemann–Liouville fractional differential equation with sequential derivatives, parameter and sign-changing singular nonlinearity, subject to nonlocal boundary conditions containing varied derivatives general Riemann–Stieltjes integrals. also present associated Green functions some their properties. In proof main results, we apply Guo–Krasnosel...