Journal of Function Spaces

Inhomogeneous Nonlinear Partial Differential Problems: Existence and Non-Existence of Solutions


Publishing date
01 Aug 2021
Status
Closed
Submission deadline
19 Mar 2021

1King Saud University, Riyadh, Saudi Arabia

2University of Palermo, Palermo, Italy

3Universidade de Brasília, Brasília, Brazil

4Yulin Normal University, Yulin, China

This issue is now closed for submissions.
More articles will be published in the near future.

Inhomogeneous Nonlinear Partial Differential Problems: Existence and Non-Existence of Solutions

This issue is now closed for submissions.
More articles will be published in the near future.

Description

It is well known that many physical systems respond to the breaking of regularities, which is often useful to determine the mathematical form of the equations dictating the behaviour of special phenomena. For example, the solvability of existence and stability problems involving nonlinear damped wave equations on symmetric domains, and double phase (p,q)-Laplacian equations in Lebesgue and Sobolev spaces, both isotropic and anisotropic, play a crucial role in particle systems, acoustics, and elasticity theory.

We know from the literature that the solvability of such equations is strongly related to the critical and asymptotic behaviour of solutions. It is known that Schrödinger type equations arise naturally in the study of dispersive phenomena, as in the case of wave equations, and are useful tools to provide precise information on the existence and non-existence of positive solutions. On the other hand, the existing regularity theory for isotropic double phase equations in Lebesgue and Sobolev spaces with constant exponents does not cover anisotropic double phase equations in Lebesgue and Sobolev spaces with variable exponents.

The aim of this Special Issue is to study the qualitative behaviour of different inhomogeneous nonlinear partial differential problems. We look to collect results establishing both the existence and non-existence of "global weak solutions" with suitable regularity properties, by focusing on control tools, namely, critical exponent values and critical parameters in the reaction term of the equations, leading to bifurcation-type theorems. Both original research and review articles are welcome.

Potential topics include but are not limited to the following:

  • Variational methods for Schrödinger type equations and (p,q)-Laplacian equations
  • Mitidieri–Pohozaev capacity method for finite in time blow-up of solutions to nonlinear equations
  • Fractional in time evolution equations
  • Critical behaviour for nonlinear evolution equations
  • Lifespan of solutions
  • Maz'ya isocapacitary inequalities for double phase equations in Orlicz-Sobolev spaces
  • Topological methods for nonlinear (p,q)-Laplacian type equations
  • Extension of the known theories to the fractional versions of Schrödinger type equations
  • Extension of the known theories to the fractional versions of (p,q)-Laplacian equations
  • Variational inequalities governed by fractional Laplacian type operators

Articles

  • Special Issue
  • - Volume 2021
  • - Article ID 5513981
  • - Research Article

Exponential Stabilization of a Swelling Porous-Elastic System with Microtemperature Effect and Distributed Delay

Abdelbaki Choucha | Salah Mahmoud Boulaaras | ... | Mohamed Abdalla
  • Special Issue
  • - Volume 2021
  • - Article ID 5551561
  • - Research Article

Nontrivial Solutions for 4-Superlinear Schrödinger–Kirchhoff Equations with Indefinite Potentials

Wei Chen | Yue Wu
  • Special Issue
  • - Volume 2021
  • - Article ID 6642957
  • - Research Article

Numerical Solution of Fractional Model of HIV-1 Infection in Framework of Different Fractional Derivatives

Sara Salem Alzaid | Badr Saad T. Alkahtani | ... | Ravi Shanker Dubey
  • Special Issue
  • - Volume 2021
  • - Article ID 6613619
  • - Research Article

Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

Hassan Eltayeb | Said Mesloub
  • Special Issue
  • - Volume 2021
  • - Article ID 5580687
  • - Research Article

Solving the Modified Regularized Long Wave Equations via Higher Degree B-Spline Algorithm

Pshtiwan Othman Mohammed | Manar A. Alqudah | ... | Khadijah M. Abualnaja
  • Special Issue
  • - Volume 2021
  • - Article ID 6674060
  • - Research Article

On a Nonhomogeneous Timoshenko System with Nonlocal Constraints

Said Mesloub | Faten Aldosari
  • Special Issue
  • - Volume 2021
  • - Article ID 6630457
  • - Research Article

Combined Effects in Singular Elliptic Problems in Punctured Domain

Imed Bachar | Habib Mâagli | Hassan Eltayeb
  • Special Issue
  • - Volume 2021
  • - Article ID 6658081
  • - Research Article

Exact Solutions of Newell-Whitehead-Segel Equations Using Symmetry Transformations

Khudija Bibi | Khalil Ahmad
  • Special Issue
  • - Volume 2020
  • - Article ID 8879366
  • - Research Article

Polynomial Decay Rate for a Coupled Lamé System with Viscoelastic Damping and Distributed Delay Terms

Nadjat Doudi | Salah Mahmoud Boulaaras | ... | Bahri Cherif
  • Special Issue
  • - Volume 2020
  • - Article ID 8835751
  • - Research Article

On Fuzzy Fixed Points and an Application to Ordinary Fuzzy Differential Equations

Eskandar Ameer | Hassen Aydi | Muhammad Arshad
Journal of Function Spaces
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