Acta Mathematicae Applicatae Sinica, English Series最新文献

In this article, we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations

where c, ε > 0; N ≥ 5; λ ∈ ℝ is a Lagrange multiplier and is unknown, h ∈ C(ℝ^N; [0;∞)); f: ℝ → ℝ is continuous function satisfying L²-subcritical growth. When ε is small enough, we get multiple normalized solutions. Moreover, we also obtain orbital stability of the solutions.

This paper is concerned with the sharp interface limit of Cauchy problem for the one-dimensional compressible Navier-Stokes/Allen-Cahn system with a composite wave consisting of the superposition of a rarefaction wave and a shock wave. Under the assumption that the viscosity coefficient and the reciprocal of mobility coefficient are directly proportional to the interface thickness, we first convert the sharp interface limit of the system into the large time behavior of the composite wave via a natural scaling. Then we prove that the composite wave is asymptotically stable under the small initial perturbations and the small strength of the rarefaction and shock wave. Finally, we show the solution of the Cauchy problem exists for all time, and converges to the composite wave solution of the corresponding Euler equations as the thickness of the interface tends to zero. The proof is mainly based on the energy method and the relative entropy.

Let A be a general expansive matrix and X be a ball quasi-Banach function space on ℝⁿ, whose certain power (namely its convexification) supports a Fefferman-Stein vector-valued maximal inequality and the associate space of whose other power supports the boundedness of the powered Hardy-Littlewood maximal operator. Let H^A_X(ℝⁿ) be the anisotropic Hardy space associated with A and X. The authors first prove that the Fourier transform of f ∈ H^A_X(ℝⁿ) coincides with a continuous function F on ℝⁿ in the sense of tempered distributions. Moreover, the authors obtain a pointwise inequality that the function F is less than the product of the anisotropic Hardy space norm of f and a step function with respect to the transpose matrix of the expansive matrix A. Applying this, the authors further induce a higher order convergence for the function F at the origin and give a variant of the Hardy-Littlewood inequality in H^A_X(ℝⁿ). All these results have a wide range of applications. Particularly, the authors apply these results, respectively, to classical (variable and mixed-norm) Lebesgue spaces, Lorentz spaces, Orlicz spaces, Orlicz-slice spaces, and local generalized Herz spaces and, even on the last four function spaces, the obtained results are completely new.

In this paper, we investigate parabolic equations involving nonlocal pseudo-relativistic Schrödinger operators (−Δ + m²)^s with s ∈ (0, 1) and mass m > 0 in bounded regions. We establish the asymptotic narrow region principle and asymptotic strong maximum principle for anti symmetric function. As applications, employing the method of moving planes, we show the asymptotical radial symmetry and monotonicity of positive solutions in an unit ball.

In this paper, we propose a new method for spread option pricing under the multivariate irreducible diffusions without jumps and with different types of jumps by the expansion of the transition density function. By the quasi-Lamperti transform, which unitizes the diffusion matrix at the initial time, and applying the small-time Itô-Taylor expansion method, we derive explicit recursive formulas for the expansion coefficients of transition densities and spread option prices for multivariate diffusions with jumps in return. It is worth mentioning that we also give the closed-form formula of spread option price whose underlying asset price processes contain a Merton jump and a double exponential jump, which is innovative compared with current literature. The theoretical proof of convergence is presented in detail.

Let w(z) be non-rational meromorphic solutions with hyper-order less than 1 to a family of higher order nonlinear delay differential equations

where a(z) is rational, (Rleft( {z,,wleft( z right)} right) = {{Pleft( {z,,w,,left( z right)} right)} over {Qleft( {z,,w,,left( z right)} right)}}) is an irreducible rational function in w with rational coefficients in z. This paper mainly show the relationships of the degree of P(z,w(z)) and Q(z,w(z)) when the above equations exist such solutions w(z). There are also some examples to show that our results are sharp.