Using the ‘monotonicity trick’ introduced by Struwe, we derive a generic theorem. It says that for a wide class of functionals, having a mountain-pass (MP) geometry, almost every functional in this class has a bounded Palais-Smale sequence at the MP level. Then we show how the generic theorem can be used to obtain, for a…
Proceedings of the Royal Society of Edinburgh Section A Mathematics Template
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About the Proceedings of the Royal Society of Edinburgh Section A Mathematics format
Proceedings of the Royal Society of Edinburgh Section A Mathematics is a peer-reviewed journal published by Cambridge University Press, covering Advanced Mathematical Modeling in Engineering, Nonlinear Partial Differential Equations, Spectral Theory in Mathematical Physics.
| Publisher | Cambridge University Press |
|---|---|
| Reference style | Numbered Numbered — [1], [2] in the text [1] A. Smith, B. Jones, and C. Lee, A representative article title, Proceedings of the Royal Society of Edinburgh Section A Mathematics 12 (2023) 45–58.
Formats any DOI in the closest standard style — Proceedings of the Royal Society of Edinburgh Section A Mathematics has no published style definition, so this is an approximation. No sign-up. |
| Publishes research in | Advanced Mathematical Modeling in Engineering Nonlinear Partial Differential Equations Spectral Theory in Mathematical Physics Stability and Controllability of Differential Equations Advanced Mathematical Physics Problems |
| ISSN | 0308-2105 |
| Citation impact (2-yr) | 0.83 |
| h-index | 99 |
| i10-index | 1,556 |
| Total citations | 65,683 |
| Top institutions publishing here | Centre National de la Recherche Scientifique |
| Journal website | www.cambridge.org |
| You get | A submission-ready PDF and the editable LaTeX source — ready to submit. |
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Most-cited papers in Proceedings of the Royal Society of Edinburgh Section A Mathematics
We study the existence of positive solutions for the nonlinear Schrödinger equation with the fractional Laplacian Furthermore, we analyse the regularity, decay and symmetry properties of these solutions.
In this paper we study the existence of radially symmetric solitary waves for nonlinear Klein–Gordon equations and nonlinear Schrödinger equations coupled with Maxwell equations. The method relies on a variational approach and the solutions are obtained as mountain-pass critical points for the associated energy functional.
Synopsis In this paper it is shown that the analysis of Titchmarsh's book [32] for regular Sturm-Liouville problems on a finite closed interval carries over readily to regular problems involving the eigenvalue parameter in the boundary condition at one end-point. The manner in which this type of problem is associated with a self-adjoint operator in…
Synopsis New mathematical objects, called H-measures, are introduced for studying oscillations and concentration effects in partial differential equations. Applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach.