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Article
Deep learning based insulator fault detection algorithm for power transmission lines
Aiming at the complex background of transmission lines at the present stage, which leads to the problem of low accuracy of insulator fault detection for small targets, a deep learning-based insulator fault det...
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Article
Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration
In this paper, we are concerned with the study of the following 2-D Schrödinger–Poisson equation with critical exponential growth $$\begin{ali...
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Article
Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation
This paper focuses on the following Kirchhoff-type problems involving fractional p-Laplacian operators and singular nonlinearities $$\begin{al...
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Article
Bifurcation and regularity of entire solutions for the planar nonlinear Schrödinger–Poisson system
This paper deals with bifurcation and regularity properties of the entire solutions of the planar nonlinear Schrödinger–Poisson system in $$\mathbb {R...
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Article
Groundstates of the Schrödinger–Poisson–Slater equation with critical growth
In this paper, we study the existence of ground state solutions for the following Schrödinger–Poisson–Slater equation: $$\begin{aligned} - \De...
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Article
Removability of Isolated Singular Points for Fourth Order Elliptic Equations with Nonstandard Growth
In this paper, we investigate the removable problem of isolated singularities for fourth order elliptic equations with nonstandard growth. Based on Moser’s iteration technique, the sufficient condition is foun...
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Article
Open AccessInfinitely many homoclinic solutions for fractional discrete Kirchhoff–Schrödinger equations
In the present paper, we consider a fractional discrete Schrödinger equation with Kirchhoff term. Through the fountain theorem and the dual fountain theorem, we obtain two different conclusions about infinitel...
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Article
Critical Schrödinger–Bopp–Podolsky System with Prescribed Mass
In this paper, we consider the critical Schrödinger–Bopp–Podolsky system with prescribed mass as follows: $$\begin{aligned} \left\{ \begin{arr...
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Article
Open AccessMulti-Peak Solutions for Coupled Nonlinear Schrödinger Systems in Low Dimensions
In this paper, we construct the solutions to the following nonlinear Schrödinger system $$\begin{aligned} {\left\{ \begin{array}{ll} -\epsilon...
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Article
Kirchhoff-Type Fractional Laplacian Problems with Critical and Singular Nonlinearities
In the present paper, we are interested in the critical Kirchhoff-type fractional Laplacian problem involving strong singularity as shown below: ...
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Article
Sufficient and Necessary Conditions for Normalized Solutions to a Choquard Equation
In this paper, our major concern is the existence of normalized solutions for a Choquard equation with a \(L^2\) ...
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Article
Kirchhoff-type problems involving the fractional p-Laplacian on the Heisenberg group
In this paper, we are interested in the existence of solutions for a class of Kirchhoff-type problems driven by a non-local integro-differential operator with the homogeneous Dirichlet boundary conditions on t...
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Article
Low Perturbations and Combined Effects of Critical and Singular Nonlinearities in Kirchhoff Problems
In this paper, we study three-dimensional Kirchhoff equations with critical growth and singular nonlinearity. We are concerned with the qualitative analysis of solutions to the following nonlocal problem ...
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Article
Normalized ground states for the critical fractional NLS equation with a perturbation
In this paper, we study normalized ground states for the following critical fractional NLS equation with prescribed mass: $$\begin{aligned} {\...
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Article
Soliton Solutions for Quasilinear Schrödinger Equations Involving Convolution and Critical Nonlinearities
In this paper, we establish the existence, multiplicity and concentration behaviour of positive solutions for quasilinear Schrödinger equations with Choquard term and critical nonlinearities:
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Article
Open AccessNonlocal Kirchhoff Problems with Singular Exponential Nonlinearity
In this paper, we first develop the fractional Trudinger–Moser inequality in singular case and then we use it to study the existence and multiplicity of solutions for a class of perturbed fractional Kirchhoff ...
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Article
Fractional Choquard-Kirchhoff problems with critical nonlinearity and Hardy potential
In this paper, we investigate the following fractional p-Kirchhoff type problem $$\begin{aligned} \left\{ \begin{array}{ll} \left( a+b[u]_{s,p...
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Article
A Uniqueness Result for Strong Singular Kirchhoff-Type Fractional Laplacian Problems
In this paper, we study the following Kirchhoff-type fractional Laplacian problem with strong singularity: $$\begin{aligned} \left\{ \begin{ar...
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Article
Quasi-Periodic Relativistic Strings in the Minkowski Space \(\mathbf{R }^{1+n}\)
In this article, we consider the motion of relativistic strings in the Minkowski space \(\mathbf{R }^{1+n}\) ...
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Article
Long Time Existence for the Bosonic Membrane in the Light Cone Gauge
This paper aims to establish the well-posedness on time interval \([0,\varepsilon ^{-\frac{1}{2}}T]\) ...