Showing papers in "Journal of Differential Equations in 2021"

TL;DR: In this article, the existence of multiple solutions by applying the Nehari manifold method along with truncation and comparison techniques and critical point theory was proved for quasilinear elliptic equations with a nonlinear boundary condition.

TL;DR: In this article, the authors studied the non-autonomous Choquard-Pekar equation, where the potential V (x ) is 1-periodic and 0 lies in a gap of the spectrum of the Schrodinger operator − Δ + V.

TL;DR: In this article, a class of singular double phase problems defined on Minkowski spaces in terms of Finsler manifolds and with right-hand sides that allow a certain type of critical growth for such problems was studied.

TL;DR: In this paper, an effective new algorithm where the memory delay is treated as the perturbation parameter was developed to meet the demand for computing the normal forms of the Hopf bifurcations of such systems, and the authors considered a diffusive predator-prey system with memory-based diffusion and Holling type-II functional response.

TL;DR: In this article, it was shown that for general linear delay-differential equations of arbitrary order including a single delay in the system's representation, spectral values of maximal multiplicity are dominant, and hence determine the asymptotic behavior of the system.

TL;DR: In this paper, the authors analyzed the global behavior of reaction-diffusion systems incorporating the pathogens' incubation period, which describes the infection of bacteria in a population, by using the operator semigroup theory and dynamical system approaches.

TL;DR: In this paper, the authors apply the steepest descent method to study the Cauchy problem for the nonlinear short-pulse equation u x t = u + 1 6 ( u 3 ) x x, u ( x, 0 ) = u 0 ( x ) ∈ H ( R ), where H( R ) = W 3, 1 (R ) ∩ H 2, 2 (R) is a weighted Sobolev space.

TL;DR: In this article, the Cauchy problem for the integrable nonlocal nonlinear Schrodinger (NNLS) equation is studied and the long-time behavior of the solution of this problem is analyzed.

TL;DR: In this article, the authors studied the Cauchy problem for the linear and semilinear Moore-Gibson-Thompson (MGT) equation in the dissipative case.

TL;DR: In this paper, a general framework for the study of differential inclusions in the Wasserstein space of probability measures is proposed, based on earlier geometric insights on the structure of continuity equations.

TL;DR: In this paper, the integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order.

TL;DR: In this article, the authors considered the stability and damping problem for the 2D Boussinesq equations with partial dissipation near a two parameter family of stationary solutions which includes Couette flow and hydrostatic balance.

TL;DR: In this article, the authors investigated the system of Schrodinger and Klein-Gordon equations with Yukawa coupling and proved the existence of pullback attractor and constructed a family of invariant Borel probability measures.

TL;DR: In this article, the authors mainly investigated the population dynamics of a general competitive parabolic system including both diffusion and advection, and provided an efficient way to determine the global dynamics by values of competition coefficients b and c.

TL;DR: In this paper, a pure energy argument (independent of spectral analysis) has been developed in more general L p framework, which enables to obtain the optimal time-decay rates and remove the smallness of low frequencies of initial data that has been required in previous studies on this problem.

TL;DR: In this paper, a general theory for atmospheric flows, based on well-defined approximation methods, is presented, which is used to describe the velocity field and to identify the heat sources required to maintain the motion of the steady atmosphere.

TL;DR: The periodic measures of the stochastic delay reaction-diffusion lattice systems are investigated in this paper, and the existence of periodic measures when the time-dependent terms of the system are periodic in time is shown.

TL;DR: In this article, a quasilinear Keller-Segel-Navier-Stokes system was proposed for coral fertilization with no-flux boundary conditions in a bounded domain with smooth boundary, where ϕ ∈ W 2, ∞ ( Ω ).

TL;DR: In this paper, Alves-Cassani-Tarsi-Yang et al. studied the problem with both critical exponential growth and strongly indefinite features when 0 lies in a gap of the spectrum of the operator − △ + V.

TL;DR: In this article, the existence of pullback attractors in non-autonomous nonlocal parabolic equations with hereditary characteristics involving bounded and unbounded delays has been proved using the Galerkin method and energy estimations.

TL;DR: In this article, a detailed bifurcation analysis of Bazykin's model with Holling II functional response and predator competition is presented, and sufficient conditions to guarantee the global asymptotical stability of the semi-trivial equilibrium or the unique positive equilibrium are also given.

TL;DR: In this paper, the authors established the existence of traveling waves for a Lotka-Volterra competition-diffusion model with a shifting habitat, assuming that the growth rate of each species is nondecreasing along the x-axis, positive near ∞ and negative near −∞, and shifting rightward at a speed c.

TL;DR: In this paper, the existence, stability, and multiplicity of steady-state solutions and periodic solutions for a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition are investigated by using Lyapunov-Schmidt reduction.

TL;DR: In this article, the authors prove the large data scattering for two models, i.e., the defocusing quintic nonlinear Schrodinger equation on R 2 × T and the def focusing cubic nonlinear Schrrodinger equations on R 3 × T.

TL;DR: It is proved the convergence of solutions and the upper semicontinuity of random attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero.

TL;DR: In this article, the authors apply the nonlinear steepest descent method to compute the long-time asymptotics of an extended modified KdV equation with decaying initial data in two transition regions, completing previous results by Liu et al.

TL;DR: In this paper, the Keller-Segel-Stokes system (⋆) was studied under the Dirichlet boundary conditions, with suitably regular functions F and Φ.

TL;DR: In this article, the authors investigated the regularity of the solution to the fractional diffusion, advection, reaction equation on a bounded domain in R 1, where the analysis is performed in the weighted Sobolev spaces, H ( a, b ) s ( I ).

TL;DR: In this article, the authors considered the problem of solving non-linear non-local Laplacian problems in unbounded domains with exterior Dirichlet conditions and developed a sliding method to derive the monotonicity and uniqueness of solutions.

TL;DR: In this article, the weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak-Orlicz) growth were studied and shown to satisfy the weak Harnack inequality with optimal exponent provided that they belong to a suitable Lebesgue or Sobolev space.