
ISSN:
1534-0392
eISSN:
1553-5258
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Communications on Pure & Applied Analysis
January 2019 , Volume 18 , Issue 1
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In this paper, for a nematic liquid crystal system, we address the space-time decay properties of strong solutions in the whole space
In this article is perfomed a global stability analysis of an infection load-structured epidemic model using tools of dynamical systems theory. An explicit Duhamel formulation of the semiflow allows us to prove the existence of a compact attractor for the trajectories of the system. Then, according to the sharp threshold
The main contribution of the N-barrier maximum principle is that it provides rather generic a priori upper and lower bounds for the linear combination of the components of a vector-valued solution. We show that the N-barrier maximum principle (NBMP, C.-C. Chen and L.-C. Hung (2016)) remains true for
We consider the following quasilinear Schrödinger equation
where
This paper is concerned with constraint minimizers of an
It is established some existence and multiplicity of solution results for a quasilinear elliptic problem driven by the Φ-Laplacian operator. One of the solutions is built as a ground state solution. In order to prove our main results we apply the Nehari method combined with the concentration compactness theorem in an Orlicz-Sobolev space framework. One of the difficulties in dealing with this kind of operator is the lost of homogeneity properties.
We consider a function $U$ satisfying a degenerate elliptic equation on $\mathbb{R}_ + ^{N + 1}: = (0, +∞)×{\mathbb{R}^N}$ with mixed Dirichlet-Neumann boundary conditions. The Neumann condition is prescribed on a bounded domain $\Omega\subset{\mathbb{R}^N}$ of class $C^{1, 1}$, whereas the Dirichlet data is on the exterior of $\Omega$. We prove Hölder regularity estimates of $\frac{U}{d_\Omega^s}$, where $d_\Omega$ is a distance function defined as $d_\Omega(z): = \text{dist}(z, {\mathbb{R}^N}\setminus\Omega)$, for $z∈\overline{\mathbb{R}_ + ^{N + 1}}$. The degenerate elliptic equation arises from the Caffarelli-Silvestre extension of the Dirichlet problem for the fractional Laplacian. Our proof relies on compactness and blow-up analysis arguments.
In the present paper, we consider the following Kirchhoff type problem
where
In this paper, we consider a viscoelastic plate equation with a logarithmic nonlinearity. Using the Galaerkin method and the multiplier method, we establish the existence of solutions and prove an explicit and general decay rate result. This result extends and improves many results in the literature such as Gorka [
An optimal condition is given for the existence of positive solutions of nonlinear Kirchhoff PDE with strong singularities. A byproduct is that $-2$ is no longer the critical position for the existence of positive solutions of PDE's with singular potentials and negative powers of the form:
Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system coupled to non-linear diffusion equations that describe the diffusion of the surfactant in the bulk phases as well as along the diffuse interface. Moreover, the surfactant concentration influences the free energy and therefore the surface tension of the diffuse interface. For this system existence of weak solutions globally in time for general initial data is proved. To this end a two-step approximation is used that consists of a regularization of the time continuous system in the first and a time-discretization in the second step.
In this paper, we prove the existence of the positive and negative solutions to p-Laplacian eigenvalue problems with supercritical exponent. This extends previous results on the problems with subcritical and critical exponents.
In this paper, we study the following critical system with fractional Laplacian:
By using the Nehari manifold, under proper conditions, we establish the existence and nonexistence of positive least energy solution of the system.
In this work, we are concerned with a class of parabolic-elliptic chemotaxis systems with the prototype given by
with nonnegative initial condition for
First, using different ideas from [
or
Next, carrying out bifurcation from "old multiplicity", we show that the corresponding stationary system exhibits pattern formation for an unbounded range of chemosensitivity
In this paper, we investigate the following a class of Choquard equation
where
Let
where
In this paper we study a class of degenerate second-order elliptic differential operators, often referred to as Fleming-Viot type operators, in the framework of function spaces defined on the
By making mainly use of techniques arising from approximation theory, we show that their closures generate positive semigroups both in the space of all continuous functions and in weighted
In addition, we show that the semigroups are approximated by iterates of certain polynomial type positive linear operators, which we introduce and study in this paper and which generalize the Bernstein-Durrmeyer operators with Jacobi weights on
As a consequence, after determining the unique invariant measure for the approximating operators and for the semigroups, we establish some of their regularity properties along with their asymptotic behaviours.
In this paper, some new results on the the regularity of Kolmogorov equations associated to the infinite dimensional OU-process are obtained. As an application, the average
The present paper is concerned with the spatial spreading speeds and traveling wave solutions of cooperative systems in space-time periodic habitats with nonlocal dispersal. It is assumed that the trivial solution
In this paper we construct the spectral expansion for the differential operator generated in
Consider the second order self-adjoint discrete Hamiltonian system
where
In this manuscript, we provide a point-wise estimate for the 3-commutators involving fractional powers of the sub-Laplacian on Carnot groups of homogeneous dimension
This paper deals with the exact controllability for a class of fractional evolution systems in a Banach space. First, we introduce a new concept of exact controllability and give notion of the mild solutions of the considered evolutional systems via resolvent operators. Second, by utilizing the semigroup theory, the fixed point strategy and Kuratowski's measure of noncompactness, the exact controllability of the evolutional systems is investigated without Lipschitz continuity and growth conditions imposed on nonlinear functions. The results are established under the hypothesis that the resolvent operator is differentiable and analytic, respectively, instead of supposing that the semigroup is compact. An example is provided to illustrate the proposed results.
For any positive decreasing to zero sequence
In this paper, we study the following quasilinear Schrödinger equation
where
In this paper, we are concerned with fractional Choquard equation
where
The finite time blow-up of solutions for 1-D NLS with oscillating nonlinearities is shown in two domains: (1) the whole real line where the nonlinear source is acting in the interior of the domain and (2) the right half-line where the nonlinear source is placed at the boundary point. The distinctive feature of this work is that the initial energy is allowed to be non-negative and the momentum is allowed to be infinite in contrast to the previous literature on the blow-up of solutions with time dependent nonlinearities. The common finite momentum assumption is removed by using a compactly supported or rapidly decaying weight function in virial identities - an idea borrowed from [
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