4.7 Article

Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

A planar Schrodinger-Newton system with Trudinger-Moser critical growth

Zhisu Liu et al.

Summary: In this paper, the existence of positive solutions to a planar Schrodinger-Newton system with general critical exponential growth is investigated. A variational approach developed in a previous work is applied to study the problem in the Sobolev space. The analysis conducted in this paper also explores the relation between different types of Schrodinger-Newton and Schrodinger-Poisson systems.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2023)

Article Mathematics

Bound states of fractional Choquard equations with Hardy-Littlewood-Sobolev critical exponent

Wen Guan et al.

Summary: In this paper, we investigate the existence and multiplicity of positive bound solutions to the fractional Choquard equation with a positive potential bounded from below. By combining variational methods and the Brouwer degree theory, we obtain extended and improved results in the case where the coefficient V(x) vanishes at infinity.

JOURNAL OF DIFFERENTIAL EQUATIONS (2023)

Article Mathematics

Multiple Positive Bound State Solutions for Fractional Schrodinger-Poisson System with Critical Nonlocal Term

Xiaoming He et al.

Summary: In this study, the existence and multiplicity of positive bound solutions for the fractional Schrodinger-Poisson system with nonlocal critical exponent are investigated using variational methods and Brouwer degree theory. These results extend and improve upon recent works with nonlocal critical exponent, and are focused on the case where λ > 0 is small.

JOURNAL OF GEOMETRIC ANALYSIS (2023)

Article Mathematics, Applied

Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction

Shuai Yuan et al.

Summary: This paper investigates the ground state solution of the fractional (N/s)-Laplacian Choquard equation. By applying weak growth conditions and refined analysis, the existence of the solution is established, and the concentration phenomenon of the solution is also studied.

FORUM MATHEMATICUM (2023)

Article Mathematics, Applied

Fractional Choquard logarithmic equations with Stein-Weiss potential

Shuai Yuan et al.

Summary: In this paper, we study a fractional p-Laplacian Choquard logarithmic equation and obtain the existence of axially symmetric solutions in both the exponential subcritical case and the exponential critical case, using variational and topological methods. We also extend the nonlinearities to more general cases compared with existing results in the exponential critical case.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2023)

Article Mathematics

Trudinger-Moser-type inequality with logarithmic convolution potentials

Silvia Cingolani et al.

Summary: We establish Moser-Trudinger-type inequalities in the presence of a logarithmic convolution potential when the domain is a ball or the entire space R2. Moreover, we characterize critical nonlinear growth rates for these inequalities to hold and for the existence of corresponding extremal functions. In addition, we show that extremal functions satisfy corresponding Euler-Lagrange equations, and we derive general symmetry and uniqueness results for solutions of these equations.

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (2022)

Article Mathematics

Quasilinear logarithmic Choquard equations with exponential growth in RN

Claudia Bucur et al.

Summary: This paper investigates the strong coupling between the N-Laplacian Schrodinger equation and higher order fractional Poisson's equations. When the order of the Riesz potential is equal to the Euclidean dimension, the system is equivalent to a nonlocal Choquard type equation. In order to define the energy and prove the existence of finite energy solutions, a suitable log-weighted variant of the Pohozaev-Trudinger inequality is introduced.

JOURNAL OF DIFFERENTIAL EQUATIONS (2022)

Article Mathematics

Another look at planar Schrodinger-Newton systems

Zhisu Liu et al.

Summary: This paper focuses on the existence of positive solutions to the planar Schrodinger-Newton system with general subcritical growth, introducing a new variational approach to study the problem in the Sobolev space H1(R2). The analysis also allows investigating the relationship between different types of Schrodinger-Newton systems, providing a new perspective on the system and potential applications in related problems.

JOURNAL OF DIFFERENTIAL EQUATIONS (2022)

Article Mathematics, Applied

Positive Solutions for a Class of Fractional Choquard Equation in Exterior Domain

Cesar T. Ledesma et al.

Summary: This work deals with the existence of positive solutions for a certain class of fractional elliptic problems. The main challenge lies in the lack of compactness due to the unboundedness of the domain and the lack of uniqueness in the solution of the limit problem. To overcome these difficulties, a splitting lemma is used along with a careful investigation of the limit profiles of the ground states of the limit problem.

MILAN JOURNAL OF MATHEMATICS (2022)

Article Mathematics, Applied

Existence of solutions for a fractional Choquard-type equation in R with critical exponential growth

Rodrigo Clemente et al.

Summary: This paper studies the existence of solutions of equations with fractional Laplacian operators and Riesz potential, and proves the existence of solutions when f has critical exponential growth.

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK (2021)

Article Physics, Mathematical

Existence and multiplicity of solutions for the fractional p-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth

Eduardo de S. Boer et al.

Summary: In this work, we investigate the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation under different growth conditions, ensuring the existence of nontrivial solutions and ground state solutions. The study also proves the existence of infinitely many solutions under subcritical growth of the nonlinearity function.

JOURNAL OF MATHEMATICAL PHYSICS (2021)

Article Mathematics, Applied

Schrodinger-Newton equations in dimension two via a Pohozaev-Trudinger log-weighted inequality

Daniele Cassani et al.

Summary: In this study, we investigate a Choquard type equation in the whole plane, where the competition between the logarithmic kernel and exponential nonlinearity requires new tools. By applying a new weighted version of the Pohozaev-Trudinger inequality, a proper function space setting is provided to prove the existence of variational, particularly finite energy solutions.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2021)

Article Mathematics, Applied

Groundstates for Choquard type equations with Hardy-Littlewood-Sobolev lower critical exponent

Daniele Cassani et al.

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2020)

Article Mathematics, Applied

Spectrum of the fractional p-Laplacian in RN and decay estimate for positive solutions of a Schrodinger equation

Leandro M. Del Pezzo et al.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2020)

Article Mathematics

The sliding methods for the fractional p-Laplacian

Leyun Wu et al.

ADVANCES IN MATHEMATICS (2020)

Article Mathematics, Applied

Choquard-type equations with Hardy-Littlewood Sobolev upper-critical growth

Daniele Cassani et al.

ADVANCES IN NONLINEAR ANALYSIS (2019)

Article Mathematics

ON THE MOSER-TRUDINGER INEQUALITY IN FRACTIONAL SOBOLEV-SLOBODECKIJ SPACES

Enea Parini et al.

JOURNAL D ANALYSE MATHEMATIQUE (2019)

Article Physics, Mathematical

Existence of positive solution for a planar Schrodinger-Poisson system with exponential growth

Claudianor O. Alves et al.

JOURNAL OF MATHEMATICAL PHYSICS (2019)

Article Mathematics

Maximum principles for the fractional p-Laplacian and symmetry of solutions

Wenxiong Chen et al.

ADVANCES IN MATHEMATICS (2018)

Article Mathematics

Higher Holder regularity for the fractional p-Laplacian in the superquadratic case

Lorenzo Brasco et al.

ADVANCES IN MATHEMATICS (2018)

Article Mathematics, Applied

MULTIPLICITY AND CONCENTRATION RESULTS FOR SOME NONLINEAR SCHRODINGER EQUATIONS WITH THE FRACTIONAL p-LAPLACIAN

Vincenzo Ambrosio et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2018)

Article Mathematics, Applied

A guide to the Choquard equation

Vitaly Moroz et al.

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS (2017)

Article Mathematics

A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian

Leandro M. Del Pezzo et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2017)

Article Mathematics

The logarithmic Choquard equation: Sharp asymptotes and nondegeneracy of the groundstate

Denis Bonheure et al.

JOURNAL OF FUNCTIONAL ANALYSIS (2017)

Article Mathematics, Applied

Local behavior of fractional p-minimizers

Agnese Di Castro et al.

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2016)

Article Mathematics, Applied

On the planar Schrodinger-Poisson system

Silvia Cingolani et al.

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2016)

Article Mathematics

Existence and concentration of ground state solutions for a critical nonlocal Schrodinger equation in R2

Claudianor O. Alves et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2016)

Article Mathematics

Global Holder regularity for the fractional p-Laplacian

Antonio Iannizzotto et al.

REVISTA MATEMATICA IBEROAMERICANA (2016)

Article Mathematics, Applied

On fractional Choquard equations

Pietro d'Avenia et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2015)

Article Mathematics

Sharp Adams-type inequalities in $\mathbb {R}^{n}$

Bernhard Ruf et al.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2012)

Article Mathematics

A sharp Trudinger-Moser type inequality for unbounded domains in R2

B Ruf

JOURNAL OF FUNCTIONAL ANALYSIS (2005)