Partial Differential Equations and Applications

2020 - 2026

Current editor(s): Zhitao Zhang

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Volume 7, issue 3, 2026

On the asymptotic behavior of solutions for a nonlinear Schrödinger system pp. 1-42

Vicente C. P. Alvarez and Ademir Pastor

The intrinsic connections between the curvature flow in Minkowski problem and gradient flow in nonlinear analysis pp. 1-16

Shen Ao, Sun Yijing and Tan Yuxin

Uniqueness and stability of normalized ground states for defocusing NLS equation with harmonic potential pp. 1-9

Chenglin Wang, Jian Zhang and Shihui Zhu

The existence of solutions of Schrödinger equations with essence resonance pp. 1-33

Chong Li

Global boundedness for generalized Schrödinger-type double phase problems in $${{\mathbb {R}}}^N$$ R N and applications to supercritical double phase problems pp. 1-33

Hoang Hai Ha, Ky Ho, Bui The Quan and Inbo Sim

Blow-up or grow-up for threshold odd solutions to NLS on the line pp. 1-15

Takahisa Inui

Multiple solutions for Schrödinger–Poisson–Slater equations with critical growth pp. 1-10

Shibo Liu

Modified scattering for the nonlinear Klein–Gordon equation pp. 1-21

Miguel Ballesteros, Gerardo Franco Córdova, Ivan Naumkin and Alexis Vaed Vázquez

Gagliardo–Nirenberg type inequality for log-concave functions and its application to nonlinear elliptic eigenvalue problems pp. 1-22

Yasuhiro Fujita, Nao Hamamuki and Ren Igarashi

Difference estimate for weak solutions to the Navier–Stokes equations in a thin spherical shell and on the unit sphere pp. 1-44

Tatsu-Hiko Miura

Existence of two thresholds in a bistable equation with nonlocal competition pp. 1-38

Matthieu Alfaro, Cédric Chane Ki Chune and Lionel Roques

Volume 7, issue 2, 2026

Asymptotic profiles of solutions for a diffusion equation with a dynamic Hardy potential pp. 1-18

Jin Takahashi and Eiji Yanagida

Integral formulation of the Kimura equation for random genetic drift pp. 1-19

Qing Liu

Stability of standing waves for all frequencies to nonlinear Schrödinger equations with potentials in one dimension pp. 1-22

Noriyoshi Fukaya, Masahiro Ikeda and Hiroaki Kikuchi

Volume 7, issue 1, 2026

Critical slowing down in bifurcating stochastic partial differential equations with red noise pp. 1-31

P. Bernuzzi, C. Kuehn and A. Morr

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

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

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

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

Tatsuya Miura and Kensuke Yoshizawa

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

Jianqing Chen, Xiaopeng Huang and Zhi-Qiang Wang

Some inequalities on Laplacian eigenvalues with Neumann type boundary data for planar disk and annulus pp. 1-25

Zhen Song and Wenming Zou

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

Yongtao Jing, Fanqin Liu, Haidong Liu and Zhaoli Liu

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

Masaya Kawamura

On the smoothness of solutions of fully nonlinear second order equations in the plane pp. 1-12

Alessandro Goffi

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

Soichiro Katayama and Kyouhei Wakasa

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

Claudio Muñoz and Nicolás Valenzuela

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

Yanina Gonzalez and A. Victoria Torres

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

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

Giuseppe Maria Coclite and Lorenzo di Ruvo

Volume 6, issue 6, 2025

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

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

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

Svetlin G. Georgiev and Gal Davidi

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

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

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

Aaron Brunk and Marvin Fritz

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

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

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

Horizontal harmonic maps between finsler manifolds pp. 1-22

Qun Chen and Haowei Lin

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

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

Nobu Kishimoto and Kiyeon Lee

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

Volume 6, issue 5, 2025

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

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

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

Michael Strunk

Volume 6, issue 4, 2025

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

Badreddine Rjaibi and Didier Auroux

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

Vladimir Georgiev and Mario Rastrelli

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

Atsuhide Ishida and Masaki Kawamoto

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

Satoshi Masaki

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

Raj Narayan Dhara

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

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

Hantaek Bae, Hyunwoo Kwon and Jaeyong Shin

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

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

Jeziel N. Correia and Claudionei P. Oliveira

Volume 6, issue 3, 2025

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

Phuong Le

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

Beckett Sanchez, Oscar Riaño and Svetlana Roudenko

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

Fabio Bagagiolo, Rossana Capuani and Luciano Marzufero

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

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

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

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

Toshiki Kondo and Mamoru Okamoto

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

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

Antoine Benoit

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

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

Vincenzo Ignazio and Michele Ricciardi

Volume 6, issue 1, 2025

Vlasov equations on directed hypergraph measures pp. 1-49

Christian Kuehn and Chuang Xu

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

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

Francescantonio Oliva and Francesco Petitta

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

Jan-Henrik Metsch

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

Simone Fagioli, Emanuela Radici and Licia Romagnoli

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

Mashael Alammari and Stanley Snelson

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