A5000446506- Nonlinear Partial Differential Equations
- Advanced Mathematical Physics Problems
- Advanced Mathematical Modeling in Engineering
- Nonlinear Differential Equations Analysis
- Nonlinear Waves and Solitons
- Geometric Analysis and Curvature Flows
- Differential Equations and Boundary Problems
- Numerical methods in inverse problems
- Contact Mechanics and Variational Inequalities
- Black Holes and Theoretical Physics
- Numerical methods in engineering
- Spectral Theory in Mathematical Physics
Hunan University of Science and Technology
2024
Huaihua University
2024
Anhui University of Science and Technology
2024
Central South University
2020-2023
Abstract We study the following fractional Choquard equation <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:msup> <m:mrow> <m:mo>(</m:mo> <m:mo>−</m:mo> <m:mi>Δ</m:mi> </m:mrow> <m:mo>)</m:mo> <m:mi>s</m:mi> </m:msup> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:mfrac> <m:mo>∣</m:mo> <m:mi>x</m:mi> <m:mi>θ</m:mi> </m:mfrac> <m:mo>=</m:mo> <m:mo stretchy="false">(</m:mo> <m:msub> <m:mi>I</m:mi> <m:mi>α</m:mi> </m:msub> <m:mo>*</m:mo> <m:mi>F</m:mi> stretchy="false">)</m:mo>...
<abstract><p>In this paper, we consider a class of critical Schrödinger-Bopp-Podolsky system. By virtue the Nehari manifold and variational methods, study existence, nonexistence asymptotic behavior ground state solutions for problem.</p></abstract>
Abstract We are concerned with the following Choquard equation: where , is p ‐Laplacian, Riesz potential, and F primitive of f which critical growth due to Hardy–Littlewood–Sobolev inequality. Under different range θ almost necessary conditions on nonlinearity in spirit Berestycki–Lions‐type conditions, we divide this paper into three parts. By applying refined Sobolev inequality Morrey norm generalized version Lions‐type theorem, some existence results established. It worth noting that our...
In this article we consider the fractional Schrodinger-Poisson system $$\displaylines{ (-\Delta)^{s} u - \mu \frac{\Phi(x/|x|)}{|x|^{2s}} +\lambda \phi = |u|^{2^*_s-2}u,\quad \text{in } \mathbb{R}^3,\cr (-\Delta)^t u^2, \quad \mathbb{R}^3, }$$ where \(s\in(0,3/4)\), \(t\in(0,1)\), \(2t+4s=3\), \(\lambda>0\) and \(2^*_s=6/(3-2s)\) is Sobolev critical exponent. By using perturbation method, establish existence of a solution for \(\lambda\) small enough. For more information see...
Abstract We consider the following Schrödinger–Bopp–Podolsky problem: $$ \textstyle\begin{cases} -\Delta u+V(x) u+\phi u=\lambda f(u)+ \vert u ^{4}u,& \text{in } \mathbb{R}^{3}, \\ \phi +\Delta ^{2}\phi = u^{2}, & \mathbb{R}^{3}. \end{cases} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mo>−</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>V</mml:mi> <mml:mo>(</mml:mo>...
In this paper, we consider the following problem: −Δpu−ζ|u|p−2u|x|p=∑i=1kIαi∗|u|pαi∗|u|pαi∗−2u+|u|p∗−2u,in RN, where N=3,4,5, p∈(1,2], ζ∈0,Λ, Λ=N−ppp, Δp:=div(|∇u|p−2∇u) is p-Laplacian operator, p∗=NpN−p critical Sobolev exponent, pαi∗=p2N+αiN−p are Hardy–Littlewood–Sobolev upper exponents, parameters αi satisfy some assumptions. First, establish refined inequality with Coulomb norm, and show corresponding best constant achieved in RN by a nonnegative function. Second, using Morrey norm...
In this paper, we study a class of critical fractional Kirchhoff-type equations with singular potential. With range parameters, propose several existence results. Our work extends the results Li and Su [Z. Angew. Math. Phys. 66, 3147 (2015)].
In this paper, we deal with the following Kirchhoff-type equation: \begin{equation*} -\bigg(1 +\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx\bigg) \Delta u +\frac{A}{|x|^{\alpha}}u =f(u),\quad x\in\mathbb{R}^{3}, \end{equation*} where $A> 0$ is a real parameter and $\alpha\in(0,1)\cup ({4}/{3},2)$. Remark that $f(u)=|u|^{2_{\alpha}^{*}-2}u +\lambda|u|^{q-2}u +|u|^{4}u$, $\lambda> 0$, $q\in(2_{\alpha}^{*},6)$, $2_{\alpha}^{*}=2+{4\alpha}/({4-\alpha})$ embedding bottom index, $6$ top index...
This paper is concerned with a nonlocal critical Neumann problem in the half space. By virtue of variational methods, global compactness theorem and Brouwer theory degree, we obtain existence multiplicity positive solutions.
The aim of this paper is to study the existence and multiplicity nonnegative solutions for following critical Kirchhoff equation involving fractional p ‐Laplace operator . More precisely, we consider where an open bounded domain with Lipschitz boundary m > 1, a 0, b dimension Sobolev exponent, parameters λ 0 < s 1 q ∞ Applying Nehari manifold, fibering maps Krasnoselskii genus theory, investigate solutions.
We consider the following parametric double-phase problem: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mfenced open="{" close=""><mml:mrow><mml:mtable class="cases"><mml:mtr><mml:mtd columnalign="left"><mml:mo>−</mml:mo><mml:mi mathvariant="normal">div</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:msup><mml:mrow><mml:mfenced open="|"...
In this paper, we consider the following Choquard equation: −Δu+u=(Iα∗F(u))F′(u)in RN where N⩾3, α∈(0,N), Iα is Riesz potential, and F(u):=1p|u|p+1q|u|q, p=N+αN q=N+αN−2 are lower upper critical exponents in sense of Hardy–Littlewood–Sobolev inequality. Based on perturbation method invariant sets descending flow, prove that above equation possesses infinitely many sign-changing solutions. Our results extend Seok [Nonlinear equations: doubly case. Appl Math Lett. 2018;76:148–156] Su [New...
Abstract In this paper, we study the Lieb's translation lemma in Coulomb–Sobolev space and then apply it to investigate existence of Pohožaev type ground state solution for elliptic equation with van der Waals potential.
We consider the following double phase problem with variable exponents: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mfenced open="{" close=""><mml:mrow><mml:mtable class="cases"><mml:mtr><mml:mtd columnalign="left"><mml:mo>−</mml:mo><mml:mi mathvariant="normal">div</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:msup><mml:mrow><mml:mfenced open="|"...
Abstract In this paper, we focus on a Kirchhoff-type equation with singular potential and critical exponent. By virtue of the generalized version Lions-type theorem Nehari–Pohožaev manifold, established existence Nehari–Pohožaev-type ground state solutions to mentioned equation. Some recent results from literature are generally improved extended.
In this paper, we deal with the existence and multiplicity of radial sign-changing solutions for fractional Schrödinger–Poisson system: (℘) (−Δ)su+u+ϕu=f(u),(−Δ)αϕ=u2,in R3(℘) where s∈(34,1), α∈(0,1) f is a continuous function. Based on perturbation approach method invariant sets descending flow, obtain system (P). addition, by applying constrained variational incorporated Brouwer degree theory, prove that (P) possesses at least one ground state solution. Furthermore, show energy exceed...