Analysis and Mathematical Physics最新文献

We study the existence of normalized solutions to the following p-Laplacian Choquard equation

having prescribed mass

where (c>0), (lambda in mathbb {R}) is the Lagrange multiplier, (*) indicates the convolution operator and (Delta _p u=textrm{div}left( |nabla u|^{p-2}nabla uright) ) denotes the usual p-Laplacian operator with (2le p<N). Under different assumptions on c and q, on the one hand, we proved the existence of the normalized ground state solution if (p_{alpha }=frac{(N+alpha )p}{2N}<q<bar{p}=frac{p(p+N+alpha )}{2N}), on the other hand, we obtained the existence of one local minimum type solution and one mountain pass solution with the prescribed mass (cin (0,c_0)) if (bar{p}<q<p_{alpha }^*=frac{(N+alpha )p}{2(N-p)}). In addition, the detailed elaboration is provided for the best constant of interpolation inequality as well as the by-product of the proof process such as a compact embedding result.

Let U be a bounded domain in (mathbb C^d) and let (L^p_a(U)), (1 le p < infty ), denote the space of functions that are analytic on (overline{U}) and bounded in the (L^p) norm on U. A point (x in overline{U}) is said to be a bounded point evaluation for (L^p_a(U)) if the linear functional (f rightarrow f(x)) is bounded in (L^p_a(U)). In this paper, we provide a purely geometric condition given in terms of the Sobolev q-capacity for a point to be a bounded point evaluation for (L^p_a(U)). This extends results known only for the single variable case to several complex variables.

In this work, the explicit expressions of coefficients involved in quasi Christoffel polynomials of order one and quasi-Geronimus polynomials of order one are determined for Jacobi polynomials. These coefficients are responsible for establishing the orthogonality of quasi-spectral polynomials of Jacobi polynomials. Additionally, the orthogonality of quasi-Christoffel Laguerre polynomials of order one is derived. In the process of achieving orthogonality, in both cases, one zero is located on the boundary of the support of the measure. This allows us to derive the chain sequence and minimal parameter sequence at the point lying at the end point of the support of the measure. Furthermore, the interlacing properties among the zeros of quasi-spectral orthogonal Jacobi polynomials and Jacobi polynomials are illustrated. Finally, we define the quasi-Christoffel polynomials of order one on the unit circle and analyze the location of their zeros for specific examples, as well as propose the problem in the general setup.

In this paper, we give a short summary of fractal calculus. We introduce the concept of fractal variation of calculus and derive the general form of the fractal Euler equation, along with an alternate form. We explore applications of the fractal Euler equation, including the optical fractal path near the event horizon of a black hole and determining the shortest distance in fractal space. Examples and illustrative plots are provided to demonstrate the detailed behavior of these equations and their practical implications.

Let (s,bin mathbb {R}). This article is devoted to establishing the Fourier-analytical characterization of the pointwise multiplier space (M(B^{s,b}_{p,q}(mathbb {R}^n))) for the logarithmic Besov space (B^{s,b}_{p,q}(mathbb {R}^n)) in the endpoint cases, that is, (p,qin {1,infty }). The authors first obtain such a characterization for the cases where (p=1) and (q=infty ) and where (p=infty ) and (q=1). Applying this, the authors then establish the duality formula (M(B^{s,b}_{p,q}(mathbb {R}^n))=M(B^{-s,-b}_{p',q'}(mathbb {R}^n)),) where (s,bin mathbb {R}), (p,qin [1,infty ]), and (p') and (q') are respectively the conjugate indices of p and q. This duality principle is further applied to establish the Fourier-analytical characterization of (M(B^{s,b}_{p,q}(mathbb {R}^n))) in the cases where (p=infty =q) and where (p=1=q).

This work derives novel exact solutions of the Biswas–Milovic nonlinear Schrödinger equation by employing the innovative Extended Modified Auxiliary Equation Mapping Technique, augmented with enhanced sensitivity analysis. The resulting bright, kink, anti-kink, and periodic soliton solutions provide deep insights into the complex dynamics of nonlinear wave propagation. To unravel the intricate behaviors of these solitons, we analyze phase trajectories, density distributions, and streamlines, with a particular focus on their sensitivity to initial conditions. Stability is rigorously evaluated through a Hamiltonian formalism, ensuring both analytical rigor and structural robustness. Collectively, these findings enrich the theoretical understanding of soliton dynamics and open new pathways for practical applications in advanced physical systems.

Fukaya and Oh studied the correspondence between pseudoholomorphic disks in (T^{*}M) which are bounded by Lagrangian sections ({L_{i}^{epsilon }}) and gradient trees in M which consist of gradient curves of ({f_{i}-f_{j}}). Here, (L_{i}^{epsilon }) is defined by (L_{i}^{epsilon }=) graph((epsilon df_{i})). They constructed approximate pseudoholomorphic disks in the case (epsilon >0) is sufficiently small. When (M=mathbb {R}) and Lagrangian sections are affine, pseudoholomorphic disks (w_{epsilon }) can be constructed explicitly. In this paper, we show that pseudoholomorphic disks (w_{epsilon }) converges to the gradient tree in the limit (epsilon rightarrow +0) when the number of Lagrangian sections is three and four.

In this paper, we define generalized monotonicity concepts related to equilibrium problems generated by trifunctions. We then study the existence of solutions to mixed equilibrium problems described as the sum of a maximal monotone trifunction and a pseudomonotone trifunction in Brézis sense. The main tools for this study are a Thikonov regularization procedure with respect to the generalized duality mapping and recession analysis adapted to trifunctions. An application consists in an existence result for a noncoercive hemivariational inequality.

The aim of this paper is to investigate the right-sided quaternionic free metaplectic transformation (QFMT) and its associated uncertainty principles (UPs) for (mathbb {R}^{2d})-dimensional quaternionic-valued signals. First, we establish the fundamental mathematical properties of the QFMT, including partial derivatives, the inversion formula, Parseval’s theorem, and the Hausdorff–Young inequality. Next, we establish various UPs within this framework, such as the Rènyi and Shannon entropy UPs and Donoho–Stark’s UP in terms of concentration. Finally, we derive (L^a)-bandlimited variant of the Donoho–Stark UP in the QFMT domain.