Partial Differential Equations and Applications

2020 - 2026

Current editor(s): Zhitao Zhang

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Volume 7, issue 1, 2026

Ground states for a system of N coupled Schrödinger equations pp. 1-24

Yongtao Jing, Fanqin Liu, Haidong Liu and Zhaoli Liu

$$2\times 2$$ 2 × 2 Laguerre-type differential operator with triangular eigenvalue pp. 1-23

Yanina Gonzalez and A. Victoria Torres

Convergence result for the short pulse equation pp. 1-30

Giuseppe Maria Coclite and Lorenzo di Ruvo

Normalized solutions to the generalized Kadomtsev–Petviashvili equations: supercritical case pp. 1-8

Jianqing Chen, Xiaopeng Huang and Zhi-Qiang Wang

Anisotropic nonlocal double phase problems with logarithmic perturbation: maximum principle and qualitative analysis of solutions pp. 1-46

Shengda Zeng, Yasi Lu, Vicenţiu D. Rădulescu and Patrick Winkert

Bounds on the approximation error for deep neural networks applied to dispersive models: nonlinear waves pp. 1-60

Claudio Muñoz and Nicolás Valenzuela

Bifurcation domains for the Serrin’s overdetermined problem in $$\mathbb {S}^n\times \mathbb {R}$$ S n × R and $$\mathbb {H}^n\times \mathbb {R}$$ H n × R pp. 1-27

G. Dai, F. Morabito and P. Sicbaldi

On the Calabi flow on quasi-Kähler manifolds pp. 1-32

Masaya Kawamura

On the existence of stationary solutions for certain systems of integro-differential equations with the double scale anomalous diffusion pp. 1-20

Vitali Vougalter and Vitaly Volpert

Stability of flat-core pinned p-elasticae pp. 1-13

Tatsuya Miura and Kensuke Yoshizawa

Dynamics of the solution for Chern–Simons–Schrödinger system under Coulomb gauge condition pp. 1-55

Jianyi Chen, Guijuan Chang, Kui Li and Zhitao Zhang

Lifespan of small solutions to semilinear hyperbolic systems in one space dimension pp. 1-33

Soichiro Katayama and Kyouhei Wakasa

Volume 6, issue 6, 2025

Rigidity for the non self-dual Chern–Simons–Schrödinger equation at the level of the soliton pp. 1-34

Benjamin Dodson

A singular perturbation problem governed by the normalized $$p(x)$$ p ( x ) -Laplacian operator pp. 1-34

João Vitor da Silva and Víctor A. B. Viloria

Stability and large-time behavior for the 2D Boussinesq system with vertical dissipation and horizontal thermal diffusion pp. 1-44

Oussama Ben Said and Mona Ben Said

Analysis and discretization of the Ohta–Kawasaki equation with forcing and degenerate mobility pp. 1-33

Aaron Brunk and Marvin Fritz

Skyrmions in two dimensional cholesteric liquid crystals pp. 1-21

Carlo Greco

Sign-changing solutions for a perturbed biharmonic equation with critical exponent pp. 1-21

Rabeh Ghoudi and Moufida Lahrach

Classical solutions for a class of Euler equations of ideal gas dynamics pp. 1-13

Svetlin G. Georgiev and Gal Davidi

Blow-up in the 2D cubic Zakharov–Kuznetsov equation in finite or infinite time pp. 1-63

Luiz Gustavo Farah, Justin Holmer, Svetlana Roudenko and Kai Yang

Global analytic solution to the IVP for the BBM equation posed on $$\mathbb {R}$$ R and $$\mathbb {T}$$ T pp. 1-26

Mikaela Baldasso and Mahendra Panthee

Semi-waves for delayed fisher-KPP equations without quasimonotonicity pp. 1-32

Hirofumi Izuhara, Harunori Monobe, Yong-Jie Syu and Chang-Hong Wu

Horizontal harmonic maps between finsler manifolds pp. 1-22

Qun Chen and Haowei Lin

Local and global well-posedness for the kinetic derivative NLS on $$\mathbb {R}$$ R pp. 1-30

Nobu Kishimoto and Kiyeon Lee

Transverse linear stability of line solitons for 2D Toda pp. 1-31

Tetsu Mizumachi

Hyperbolic nonlinear Schrödinger equations on $${\mathbb {R}}\times {\mathbb {T}}$$ R × T pp. 1-28

Engin Başakoğlu, Chenmin Sun, Nikolay Tzvetkov and Yuzhao Wang

A concentration phenomenon for a semilinear Schrödinger equation with periodic self-focusing core pp. 1-11

Mónica Clapp, Alberto Saldaña and Andrzej Szulkin

Large-time existence results for the nonlocal NLS around ground state solutions pp. 1-23

Hideo Takaoka and Toshihiro Tamaki

Volume 6, issue 5, 2025

Large time asymptotics for the fractional Schrödinger equation with subcritical derivative nonlinearities pp. 1-22

Nakao Hayashi and Pavel I. Naumkin

Existence of ground state solutions for the critical case of Berestycki-Lions’ theorem pp. 1-26

Shinji Adachi and Tatsuya Watanabe

On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule pp. 1-42

Scipio Cuccagna and Masaya Maeda

Gradient regularity for widely degenerate elliptic partial differential equations pp. 1-51

Michael Strunk

Volume 6, issue 4, 2025

Fractional Sobolev spaces for the singular-perturbed Laplace operator in the $$L^p$$ L p setting pp. 1-40

Vladimir Georgiev and Mario Rastrelli

Speckle noise removal in color images using a generalized nonstandard fourth-order variational method pp. 1-30

Badreddine Rjaibi and Didier Auroux

Existence and uniqueness of large solutions of a degenerate and/or singular semilinear elliptic problem pp. 1-17

Raj Narayan Dhara

Partial classification of the large-time behavior of solutions to cubic nonlinear Schrödinger systems pp. 1-52

Satoshi Masaki

On Schrödinger equation with square and inverse-square potentials pp. 1-11

Atsuhide Ishida and Masaki Kawamoto

Local and global solutions to Stokes-Magneto equations with fractional dissipations pp. 1-23

Hantaek Bae, Hyunwoo Kwon and Jaeyong Shin

On the regularity of Dirac eigenfunctions pp. 1-18

Tuyen Vu

New results for a class of quasilinear Schrödinger equations pp. 1-18

Taib Talbi

Multiplicity results for a nonlocal system with critical growth pp. 1-15

Jeziel N. Correia and Claudionei P. Oliveira

Correction to “The unique continuation property for second order evolution PDEs” [Partial Differ. Equ. Appl. 2, 67 (2021), 46 p] with additional comments pp. 1-8

Mourad Choulli

Volume 6, issue 3, 2025

Asymptotic behavior for the dissipative nonlinear Schrödinger equations under mass supercritical setting pp. 1-14

Gaku Hoshino

Multiplicity of solutions for a nonlinear Schrödinger system with three wave interaction pp. 1-14

Tomoharu Kinoshita and Yuki Osada

A zero-sum differential game for two opponent masses pp. 1-23

Fabio Bagagiolo, Rossana Capuani and Luciano Marzufero

Bifurcations and dynamical behaviors for a generalized Maginu model with distributed delay pp. 1-24

Xiaowei Ju

Classification of weak and unbounded traveling wave solutions for a Porous–Fisher-KPP equation pp. 1-24

Yu Ichida

On the well-posedness of the periodic fractional Schrödinger equation pp. 1-28

Beckett Sanchez, Oscar Riaño and Svetlana Roudenko

Longtime behavior of a free boundary model with nonlocal diffusion in online social networks pp. 1-26

Phuong Le

The existence of $$L^2$$ L 2 -constrained solutions for Kirchhoff equations with $$L^2$$ L 2 -critical general nonlinearity pp. 1-25

Hongyu Ye and Jiahui Yin

Volume 6, issue 2, 2025

A second-order Mean Field Games model with controlled diffusion pp. 1-34

Vincenzo Ignazio and Michele Ricciardi

Convergence of one-dimensional stationary mean field games with vanishing potential pp. 1-16

Yiru Cai, Haobo Qi, Xifeng Su and Yi Tan

Degenerate free boundary problems with oscillatory singularities pp. 1-16

Aelson Sobral, Eduardo V. Teixeira and José Miguel Urbano

Multiple solutions for superlinear fractional p-Laplacian equations pp. 1-20

Antonio Iannizzotto, Vasile Staicu and Vincenzo Vespri

On the sharp constants in the regional fractional Sobolev inequalities pp. 1-20

Rupert L. Frank, Tianling Jin and Wei Wang

Adaptive sensitivity control for a feedback loop and a consensus model with unknown delay pp. 1-20

Jan Haskovec

Norm inflation for a higher-order nonlinear Schrödinger equation with a derivative on the circle pp. 1-14

Toshiki Kondo and Mamoru Okamoto

Regular solution to hyperbolic boundary value problems without regularization pp. 1-38

Antoine Benoit

Volume 6, issue 1, 2025

Existence and stability of near-constant solutions of variable-coefficient scalar field equations pp. 1-28

Mashael Alammari and Stanley Snelson

A construction of peak solutions by a local mountain pass approach for a nonlinear Schrödinger system with three wave interaction pp. 1-26

Yuki Osada and Yohei Sato

Modeling and mathematical analysis of the clogging phenomenon in filtration filters installed in aquaria pp. 1-71

Ken Furukawa and Hiroyuki Kitahata

On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis pp. 1-31

Simone Fagioli, Emanuela Radici and Licia Romagnoli

Instability of stationary solutions for double power nonlinear Schrödinger equations in one dimension pp. 1-23

Noriyoshi Fukaya and Masayuki Hayashi

A uniqueness result for the d-dimensional magnetohydrodynamics equations with fractional dissipation in Besov spaces pp. 1-27

Hua Qiu, Xia Wang and Zheng-an Yao

Singular elliptic PDEs: an extensive overview pp. 1-82

Francescantonio Oliva and Francesco Petitta

Vlasov equations on directed hypergraph measures pp. 1-49

Christian Kuehn and Chuang Xu

Axially symmetric Willmore minimizers with prescribed isoperimetric ratio pp. 1-60

Jan-Henrik Metsch