{"title":"On a class of Schrödinger–Kirchhoff-double phase problems with convection term and variable exponents","authors":"Noureddine Moujane, Mohamed El Ouaarabi","doi":"10.1016/j.cnsns.2024.108453","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate the existence of solutions for double-phase problems with variable exponents of the Kirchhoff–Schrödinger type, incorporating a convection term. By imposing certain assumptions and utilizing the topological degree for a class of <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math>-demicontinuous operators, along with the Galerkin method within the framework of Musielak–Orlicz–Sobolev spaces, we establish the existence of strong generalized solutions and weak solutions for the problems under consideration.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"18 1","pages":""},"PeriodicalIF":3.4000,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.cnsns.2024.108453","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, we investigate the existence of solutions for double-phase problems with variable exponents of the Kirchhoff–Schrödinger type, incorporating a convection term. By imposing certain assumptions and utilizing the topological degree for a class of (S+)-demicontinuous operators, along with the Galerkin method within the framework of Musielak–Orlicz–Sobolev spaces, we establish the existence of strong generalized solutions and weak solutions for the problems under consideration.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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