Communications on Pure & Applied Analysis
January 2020 , Volume 19 , Issue 1
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We are concerned with the coexistence states of the diffusive Lotka-Volterra system of two competing species when the growth rates of the two species depend periodically on the spacial variable. For the one-dimensional problem, we employ the generalized Jacobi elliptic function method to find semi-exact solutions under certain conditions on the parameters. In addition, we use the sine function to construct a pair of upper and lower solutions and obtain a solution of the above-mentioned system. Next, we provide a sufficient condition for the existence of pulsating fronts connecting two semi-trivial states by applying the abstract theory regarding monotone semiflows. Some numerical simulations are also included.
In this paper, we consider the subsolutions of the Monge-Ampère type equations
This paper deals with changes of variables, and the exact bifurcation diagrams for a class of self-similar equations. Our first result is a change of variables which transforms radial
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the
A delayed reaction-diffusion virus model with a general incidence function and spatially dependent parameters is investigated. The basic reproduction number for the model is derived, and the uniform persistence of solutions and global attractively of the equilibria are proved. We also show the global attractivity of the positive equilibria via constructing Lyapunov functional, in case that all the parameters are spatially independent. Numerical simulations are finally conducted to illustrate these analytical results.
We obtain estimates for sums of eigenvalues of the free plate under tension in terms of the dimension of the ambient space, the volume of the domain, and the tension parameter. We consequently obtain similar estimates for the eigenvalues. Our results generalize those of Kröger for the free membrane contained in [
We are concerned with nonlinear fractional Choquard equations involving critical growth in the sense of the Hardy-Littlewood-Sobolev inequality. Without the Ambrosetti-Rabinowitz condition or monotonicity condition on the nonlinearity, we establish the existence of radially symmetric ground state solutions.
We show the existence and
We address small volume-fraction asymptotic properties of a nonlocal isoperimetric functional with a confinement term, derived as the sharp interface limit of a variational model for self-assembly of diblock copolymers under confinement by nanoparticle inclusion. We introduce a small parameter
The morbidostat is a bacteria culture device that progressively increases antibiotic drug concentration and maintains a constant challenge for study of evolutionary pathway. The operation of a morbidostat under serial transfer has been analyzed previously. In this work, the global dynamics for the operation of a morbidostat under continuous dilution is analyzed. The device switches between drug on and drug off modes according to a simple threshold algorithm. We prove the extinction and uniform persistence of all species with both forward and backward mutations. Numerical simulations for the case of logistic growth and the Hill function for drug inhibition are also presented.
We are concerned with the existence and multiplicity of component-wise positive solutions for nonlinear system of Hammerstein integral equations with the weighted functions and the associated nonlinear eigenvalue problem. Our discussions are based on the product formula of fixed point index on product cones and the fixed point index theory. Moreover, we establish the existence and multiplicity of component-wise positive solutions for the associated nonlinear systems of second-order ordinary differential equations under the mixed boundary value conditions.
We prove the existence of positive classical solutions for the
The existence, non-existence and qualitative properties of time periodic pyramidal traveling front solutions for the time periodic Lotka-Volterra competition-diffusion system have already been studied in
In this paper we prove the existence and multiplicity of subharmonic solutions for nonlinear equations involving the singular
This work studies the effects of rapid oscillations (with respect to time) of the forcing term on the long-time behaviour of the solutions of the Swift-Hohenberg equation. More precisely, we establish three kinds of averaging principles for the Swift-Hohenberg equation, they are averaging principle in a time-periodic problem, averaging principle on a finite time interval and averaging principle on the entire axis.
This paper is devoted to study the following systems of coupled elliptic equations with quadratic nonlinearity
which arises from second- harmonic generation in quadratic optical media. We assume that the potential functions
In this paper we are interested in the following critical coupled Hartree system
In this paper we define a more general convolution product (associated with Gaussian processes) of functionals on the function space
This paper is concerned with a class of biharmonic elliptic differential inclusion in
Recently, in [
We consider the initial value problem (IVP) associated with the Schrödinger-Debye system posed on a $d$-dimensional compact Riemannian manifold
This paper is devoted to the study of a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions. Based on the Faedo-Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we first establish two local existence theorems of weak solutions. By the construction of a suitable Lyapunov functional, we next prove a blow up result and a decay result of global solutions.
We prove the weak maximum principle for second-order elliptic and parabolic equations in divergence form with the conormal derivative boundary conditions when the lower-order coefficients are unbounded and domains are beyond Lipschitz boundary regularity. In the elliptic case we consider John domains and lower-order coefficients in
We consider the boundary value problem
This paper focuses on almost-periodic time-dependent perturbations of a class of almost-periodically forced systems near non-hyperbolic equilibrium points in two cases: (a) elliptic case, (b) degenerate case (including completely degenerate). In elliptic case, it is shown that, under suitable hypothesis of analyticity, nonresonance and nondegeneracy with respect to perturbation parameter
In this paper we consider the semi-classical solutions of a massive Dirac equations in presence of a critical growth nonlinearity
Under a local condition imposed on the potential
We prove a sharp resolvent estimate in scale invariant norms of Amgon–Hörmander type for a magnetic Schrödinger operator on
with large potentials
The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schrödinger, wave and Klein–Gordon flows associated to
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