Anisotropic nonlocal double phase problems with logarithmic perturbation: maximum principle and qualitative analysis of solutions

Anisotropic nonlocal double phase problems with logarithmic perturbation: maximum principle and qualitative analysis of solutions

Článek WoS

In this paper, we study multivalued nonlocal elliptic problems driven by the fractional double phase operator with variable exponents and omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-logarithmic perturbation formulated by -Delta Hsu is an element of F(x,u)in Omega,u=0onRN\Omega.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\left\{ \begin{array}{ll} \left( -\Delta \right) s_{\mathcal {H}} u \in \mathcal {F}(x,u) \quad & \text {in } \Omega ,\\ u=0& \text {on } \mathbb {R}N\setminus \Omega . \end{array}\right. } \end{aligned}$$\end{document}We are going to establish maximum principles for the fractional perturbed double phase operator and show the boundedness of weak solutions to the above problem. Finally, under appropriate assumptions we discuss the existence of infinitely many small (non-negative) weak solutions to a single-valued nonlocal double phase problem.

In this paper, we study multivalued nonlocal elliptic problems driven by the fractional double phase operator with variable exponents and omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-logarithmic perturbation formulated by -Delta Hsu is an element of F(x,u)in Omega,u=0onRN\Omega.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\left\{ \begin{array}{ll} \left( -\Delta \right) s_{\mathcal {H}} u \in \mathcal {F}(x,u) \quad & \text {in } \Omega ,\\ u=0& \text {on } \mathbb {R}N\setminus \Omega . \end{array}\right. } \end{aligned}$$\end{document}We are going to establish maximum principles for the fractional perturbed double phase operator and show the boundedness of weak solutions to the above problem. Finally, under appropriate assumptions we discuss the existence of infinitely many small (non-negative) weak solutions to a single-valued nonlocal double phase problem.

A priori bounds; De Giorgi's iteration; Fractional logarithmic double phase operator; Localization method; Maximum principle; Multivalued problem; Variational methods

A priori bounds; De Giorgi's iteration; Fractional logarithmic double phase operator; Localization method; Maximum principle; Multivalued problem; Variational methods

ZENG, S.; LU, Y.; RADULESCU, V.; WINKERT, P.

2026

05.02.2026

Partial Differential Equations and Applications

7

1

Švýcarská konfederace

46

https://link.springer.com/article/10.1007/s42985-026-00373-2