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Showing papers in "Journal of Differential Equations in 2020"


Journal ArticleDOI
TL;DR: In this paper, the existence and properties of ground states for the nonlinear Schrodinger equation with combined power nonlinearities were studied under different assumptions on q p, a > 0, and μ ∈ R. The authors proved several existence and stability/instability results.

182 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient and proved the existence of a weak solution by applying the theory of pseudomonotone operators.

106 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the uniqueness of a complex-valued scalar function over a smooth compact Riemannian manifold with smooth boundary, given the Dirichlet-to-Neumann map, in a suitable sense, for the elliptic semi-linear equation − Δ g u + V (x, u ) = 0.

106 citations


Journal ArticleDOI
TL;DR: In this paper, a variational and analytic technique was developed to prove that the following planar Schrodinger-Poisson system admits a nontrivial solution and a ground state solution possessing the least energy in the axially symmetric functions space.

76 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the averaging principle for stochastic differential equations with slow and fast time-scales, where the drift coefficients satisfy local Lipschitz conditions with respect to the slow variables, and the coefficients in the slow equation depend on time t and ω.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the sensitivity of linear quadratic optimal control problems governed by general evolution equations with bounded or admissible control operator is analyzed and it is shown that if the problem is stabilizable and detectable, the solution of the extremal equation can be bounded by the right hand side including initial data with the bound being independent of the time horizon.

67 citations


Journal ArticleDOI
TL;DR: In this article, the authors formulate and analyze a mosquito population suppression model consisting of two sub-equations constantly switching between each other, where the waiting period T between two consecutive releases is greater than the sexual lifespan T of the sterile mosquitoes.

63 citations


Journal ArticleDOI
TL;DR: In this article, a singularly perturbed Schrodinger-Poisson system with a small positive parameter was studied, and it was shown that there exists a constant e 0 > 0 determined by V and f such that for e ∈ ( 0, e 0 ] the above system admits a semiclassical ground state solution v ˆ e with exponential decay at infinity.

63 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that if the topological entropy of a non-autonomous dynamical system (X, f n } n = 1 + ∞ ) vanishes, then so does that of its induced system (M ( X ), f n ) n = 0.

62 citations


Journal ArticleDOI
TL;DR: In this paper, the authors considered global existence of classical solutions to the following kinetic model of pattern formation (0.1) in the two-dimensional setting with any μ ≥ 0 and showed that the global solution is uniform-in-time bounded if either 1 / γ satisfies certain polynomial growth condition or μ > 0.

60 citations


Journal ArticleDOI
TL;DR: In this paper, a stochastic algal growth model with the explicit incorporation of season-dependent light and nutrient availability is proposed and investigated, and the authors prove the existence and global attractiveness of a positive stochastically periodic solution when 〈 λ 〉 ϖ > 0 by constructing suitable Lyapunov functions.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the initial boundary value problem of pseudo-parabolic equation with singular potential and obtained global existence, asymptotic behavior and blowup of solutions with initial energy J( u 0 ) ≤ d.

Journal ArticleDOI
TL;DR: In this paper, the existence of ground state solutions and infinitely many geometrically distinct solutions under the weaker super-quadratic condition lim | u | → ∞ ⁡ ∫ 0 u f ( x, s ) d s u 2 = ∞, a.k.a.

Journal ArticleDOI
TL;DR: In this paper, the propagation dynamics of a nonlocal dispersal Fisher-KPP equation in a time-periodic shifting habitat were studied and the existence, uniqueness and global exponential stability of periodic forced waves were established.

Journal ArticleDOI
TL;DR: In this article, the eigenvalues and minimizers of a fractional non-standard growth problem were studied and several properties on these quantities and their corresponding eigenfunctions were proved.

Journal ArticleDOI
TL;DR: In this article, the authors considered the initial value problem to the Camassa-Holm equation in the real-line case and proved that the data-to-solution map of this problem is not uniformly continuous in nonhomogeneous Besov spaces in the sense of Hadamard.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Cauchy problem is basically ill-posed for the L ∞ -initial data in the class of weak entropy solutions, and that there are infinitely many measure-valued solutions for a vast set of initial data.

Journal ArticleDOI
TL;DR: Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space in this article, where the authors introduce the idea of Poincare sections, and prove that if the measure is PS-ergodic, then it is ergodic.

Journal ArticleDOI
TL;DR: In this article, the uniqueness and nondegeneracy of positive solutions to the singularly perturbation problem (0.1) were established for ϵ > 0 sufficiently small.

Journal ArticleDOI
TL;DR: In this paper, a haptotaxis system proposed as a model for oncolytic virotherapy, accounting for interaction between uninfected cancer cells, infected cancer cells and extracellular matrix (ECM) was studied.

Journal ArticleDOI
TL;DR: In this article, Chen et al. considered a planar Schrodinger-Poisson system and obtained the existence of a nontrivial solution or a ground state solution of Nehari-type and infinitely many solutions under weak assumptions on V and f.

Journal ArticleDOI
Jianshe Yu1
TL;DR: In this article, the existence and stability of a unique and exact two periodic orbits of an ordinary differential equation model for the interaction of wild and the released sterile mosquitoes, which consists of two sub-equations constantly switching each other, was studied.

Journal ArticleDOI
TL;DR: In this article, a host-generalist parasitoid model with Holling II functional response was studied and the authors showed that the model can undergo a sequence of bifurcations including cusp, focus and elliptic types degenerate Bogdanov-Takens bifurocations of codimension three, and a degenerate Hopf Bifurcation of codeimension at most two as the parameters vary, and the model exhibits rich dynamics such as the existence of multiple coexistent steady states, multiple coexisting periodic orbits, homoclinic

Journal ArticleDOI
TL;DR: In this paper, a viscoelastic plate equation of Moore-Gibson-Thompson type coupled with two different kinds of thermal laws, namely, the usual Fourier one and the heat conduction law of type III, is shown to generate a contraction semigroup of solutions on a suitable Hilbert space.

Journal ArticleDOI
TL;DR: In this paper, the initial value problem for the complex short pulse equation with a Wadati-Konno-Ichikawa type Lax pair was considered, and it was shown that the solution has a parametric expression in terms of the solution of 2 × 2 -matrix Riemann-Hilbert problem from which an implicit one-soliton solution is obtained on the discrete spectrum.

Journal ArticleDOI
TL;DR: In this paper, the normal form up to the third order for the Hopf-steady state bifurcation of a general system of partial functional differential equations (PFDEs) in a bounded spatial region of any dimension, is derived based on the center manifold and the normal-form theories of PFDEs.

Journal ArticleDOI
TL;DR: In this paper, a nonlinear bi-harmonic equation Δ 2 u − Δ u + ( λ a + 1 ) u = | u | p − 2 u on G = ( V, E ) is considered and it is shown that for any λ > 1 and p > 2, the equation admits a ground state solution u λ.

Journal ArticleDOI
TL;DR: In this paper, the authors prove sufficient conditions for the existence of trajectory statistical solutions for autonomous evolution equations and establish that the constructed trajectories possess invariant property and satisfy a Liouville type equation.

Journal ArticleDOI
TL;DR: In this paper, higher order Calderon-Zygmund estimates for the p-Laplace equation were obtained for the planar case and the quasi-Banach case for all possible ϱ, q ∈ ( 0, 1 ) and all reasonable ϱ, q ǫ ∈( 0, ∞ ], respectively.

Journal ArticleDOI
TL;DR: In this article, the authors investigated an attraction-repulsion chemotaxis system with logistic source under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary and showed that the system possesses global classical solution or at least one global weak solution.