Showing papers in "Journal of Differential Equations in 2022"

TL;DR: In this paper , a new class of quasilinear elliptic equations driven by the double phase operator with variable exponents is introduced, and the existence and uniqueness of corresponding equations with right-hand sides that have gradient dependence (so-called convection terms) under very general assumptions on the data is shown.

TL;DR: In this paper , the authors studied the initial-boundary value problem of a three-species spatial food chain model and established the global stability of the prey-only steady state, semi-coexistence and coexistence steady states.

TL;DR: In this paper , a quasi-linear hyperbolic parabolic system of persistence and endogenous chemotaxis was modeled for vasculogenesis and it was shown that the solution of the concerned system will locally and asymptotically converge to a nonlinear diffusion wave.

TL;DR: In this article , the authors investigated the spatiotemporal dynamics of a diffusive plant-water model in an arid flat environment and found that the system has the properties of Turing-Hopf bifurcation.

TL;DR: In this paper , a delay differential equation model was developed to study the suppression of wild mosquito population by releasing Wolbachia-infected male mosquitoes with a release period T =τ/m, where m is a positive integer.

TL;DR: In this article , sufficient conditions for the existence of invariant sample measures for random dynamical systems via the approach of global random attractors were proved and generalized to the random Liouville type theorem.

TL;DR: In this article , the authors give a construction of u 0 ∈ B p , ∞ σ such that the corresponding solution to the Camassa-Holm equation starting from u 0 is discontinuous at t = 0 in the metric of B p, ∞ , σ .

TL;DR: In this paper , the exact Riemann solutions are constructed in completely explicit forms for the drift-flux equations of the one-dimensional inviscid, compressible and isentropic liquid-gas two-phase flow model in an inclined pipeline under gravity.

TL;DR: In this paper, the authors give a construction of u 0 ∈ B p, ∞ σ such that the corresponding solution to the Camassa-Holm equation starting from u 0 is discontinuous at t = 0 in the metric of B p, ∞, σ.

TL;DR: In this paper , the authors studied the interplay between the functional response of Holling type IV and both strong and weak Allee effects in a predator-prey system, and they showed that the transition between Allee effect in prey provides a simple regime shift in ecology.

TL;DR: In this article , the authors study the long-time asymptotic behavior of the focusing Fokas-Lenells (FL) equation with generic initial data in a Sobolev space which supports bright soliton solutions.

TL;DR: In this paper , the general fractional derivatives are defined as compositions of the first order derivative and a convolution integral with a non-negative and non-increasing kernel, and some estimates for these derivatives acting on the nonnegative functions are employed for derivation of the comparison principles in several different forms.

TL;DR: In this paper , the authors employ the ∂ ¯ -steepest descent method to investigate the Cauchy problem of the complex short pulse (CSP) equation with initial conditions in weighted Sobolev space H ( R ) .

TL;DR: In this paper, the multiplicity of multi-bump solutions for the nonlinear magnetic Choquard equation was studied using variational methods, and it was shown that if the zero set of V has several isolated connected components Ω 1, ⋯, Ω k such that the interior of Ω j is non-empty and ∂ Ω h is smooth, then for λ > 0 large enough, the above equation has at least 2 k − 1 multibump solutions.

TL;DR: In this article , the authors considered a double phase Dirichlet problem with both convex and nonconvex unilateral constraints (variational-hemivariational inequality) and established the existence of a nontrivial bounded solution.

TL;DR: In this paper , the existence of positive solutions to the following planar Schrödinger-Newton system with general subcritical growth was studied in the Sobolev space H1(R2).

TL;DR: In this article , the multiplicity of multi-bump solutions for the nonlinear magnetic Choquard equation was studied using variational methods, and it was shown that if the zero set of V has several isolated connected components Ω 1, ⋯ , Ω k such that the interior of Ω j is non-empty and ∂ ∂ ǫ j is smooth, then for λ > 0 large enough, the above equation has at least 2 k − 1 multibump solutions.

TL;DR: In this paper , the authors studied inverse problems for semilinear elliptic equations with fractional power type nonlinearities and showed that the results of [24], [23] remain valid for general power types.

TL;DR: In this article , initial value problems for semilinear wave equations with spatial weights in one space dimension were studied and the lifespan estimates of classical solutions for compactly supported data were established in all the cases of polynomial weights.

TL;DR: In this paper, the authors studied the existence of ground states and nontrivial solutions for the following Hamiltonian elliptic system with critical exponential growth, where the strongly indefinite features together with the critical exponent bring some new difficulties in their analysis.

TL;DR: In this paper , a direct approach and an approaching argument to seek Cerami sequences for the energy functional and estimate the minimax levels of such sequences was developed, and the existence of ground states and nontrivial solutions for the above system as well as the following system in bounded domain was obtained.

TL;DR: In this paper , the convergence of the nonlocal to the local degenerate Cahn-Hilliard equation was studied. But only non-degenerate mobilities were treated.

TL;DR: In this article , the authors studied the asymptotic behavior of endemic equilibrium solutions of a diffusive epidemic model in spatially heterogeneous environment when the diffusion rates d S of the susceptible and d I of the infected groups approach zero.

TL;DR: In this paper , the authors consider a class of cooperative reaction-diffusion systems with free boundaries in one space dimension, where the diffusion terms are nonlocal, given by integral operators involving suitable kernel functions, and they are allowed not to appear in some of the equations in the system.

TL;DR: In this article , the nonsmooth maximum principle derived in [33] for global minimizers of an optimal control problem governed by a controlled nonconvex sweeping process, is generalized in several directions.

TL;DR: In this article , the authors showed that the inhibition phenomenon of the Rayleigh-Taylor instability by a horizontal magnetic field can be rigorously verified in the (nonlinear) inhomogeneous, incompressible, inviscid case with velocity damping.

TL;DR: In this article , the authors derived explicit formulas of the normal form that can be applied for both functional differential equations and partial differential equations with or without nonlocal effects in a bounded spatial domain.

TL;DR: In this article , it was shown that for any reasonably regular initial data, the corresponding initial-boundary value problem for the spatially three-dimensional Stokes system possesses a globally bounded classical solution, and that this solution stabilizes toward the corresponding spatially homogeneous equilibrium with the explicit convergence rates for the cases r < 0, r = 0 and r > 0 .

TL;DR: In this paper , the authors study distribution dependent stochastic differential equations driven simultaneously by fractional Brownian motion with Hurst index H>12 and standard Brownians motion and establish the existence and uniqueness theorem for solutions of the distributions of the distribution dependent SDEs by utilizing the Carathéodory approximation.

TL;DR: In this paper, the authors studied inverse problems for semilinear elliptic equations with fractional power type nonlinearities, where the solution for a corresponding linear equation is not known.