Acta Applicandae Mathematicae最新文献

This work is devoted to study the existence of least energy sign-changing solutions for a nonlocal weighted Schrödinger-Kirchhoff problem in the unit ball (B) of (mathbb{R}^{N}), (N>2). The non-linearity of the equation is assumed to have exponential growth in view of Trudinger-Moser type inequalities. In order to obtain our existence result, we use the constrained minimization in Nehari set, the quantitative deformation Lemma and degree theory results.

Introducing a logarithmic pressure, we analyze the phenomenon of concentration and the formation of delta-shocks for the generalized Chaplygin gas dynamics. We first solve the Riemann problem for the logarithmic perturbed model and construct the solutions with four kinds of structures (R_{1}+R_{2}), (R_{1}+S_{2}), (S_{1}+R_{2}) and (S_{1}+S_{2}). Then it is shown that when the logarithmic pressure vanishes, the limits of the Riemann solutions for the logarithmic perturbed model are just these of the generalized Chaplygin gas dynamics. In particular, when the initial data satisfy some certain conditions, the (S_{1}+S_{2}) solution of the logarithmic perturbed model tends to the delta-shock solution of the generalized Chaplygin gas dynamics. Finally, some numerical results exhibit the process of formation of delta-shocks.

Principal and nonprincipal solutions of differential equations play a critical role in studying the qualitative behavior of solutions in numerous related differential equations. The existence of such solutions and their applications are already documented in the literature for differential equations, difference equations, dynamic equations, and impulsive differential equations. In this paper, we make a contribution to this field by examining impulsive dynamic equations and proving the existence of such solutions for second-order impulsive dynamic equations. As an illustration, we prove the famous Leighton and Wong oscillation theorems for impulsive dynamic equations. Furthermore, we provide supporting examples to demonstrate the relevance and effectiveness of the results.

We provide a result on the existence of a positive periodic solution for the following class of delay equations

In particular, we find an infinite family of disjoint intervals having the following property: if the delay is within one of these intervals, then the equation admits a non-trivial and even (2r)-periodic solution. Furthermore, the length of these intervals is constant and depends on the size of the term (|f'(eta )|), where (eta ) is the unique positive equilibrium point of the equation. Consequently, we can find periodic solutions for arbitrarily large delays.

General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic (mathrm {L}_{p}) estimates of maximal regularity type are carried over from ℛ-bounds of the family of solution operators (ℛ-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier-Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.

In this work, we study a class of degenerate Dirichlet problems, whose prototype is

where (Omega ) is a bounded open subset of (mathbb{R}^{N}). (0<gamma <1), (0<theta leq 1) and (0leq beta <1). We prove existence of bounded solutions when (f) and (c) belong to suitable Lebesgue spaces. Moreover, we investegate the existence of renormalized solutions when the function (f) belongs only to (L^{1}(Omega )).

The aim of this paper is to conduct two group reductions for matrix spectral problems simultaneously. We formulate reduced Ablowitz-Kaup-Newell-Segur matrix spectral problems under two local group reductions, and construct associated hierarchies of matrix integrable models, which keep the corresponding zero curvature equations invariant. In this way, various integrable models can be generated via zero curvature equations.

A new Bresse system with hybrid damping coming from elasticity, thermoelasticity, and viscoelasticity, is analyzed. The uniform (exponential) stabilization of semigroup solution is proved under the dynamic response of each hybrid damping effect.

The global well-posedness of the 3D inviscid MHD-Boussinesq system, with large axisymmetric initial data, in the Sobolev space (H^{m}) is given. To overcome difficulties that arise in the time-uniform (H^{1}) estimate, a reformulated system of good unknowns is discovered and an intermediate estimate is shown. Based on the reformulated system, a Beale-Kato-Majda-type criterion of the inviscid MHD-Boussinesq system is verified. Then higher-order estimates are concluded by the classical energy method and estimates of commutators. At last, we show the (H^{m}) norm of the global-in-time solution temporally grows no faster than a four times exponential function ((forall min mathbb{N})).

In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation characterized by the nontrivial interactions between nonlocality and the regimes of low and high frequencies are studied and suitable numerical investigations are exposed.