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We prove two explicit bounds for the multiplicities of Steklov eigenvalues $σ_{k}$ on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index $k$ of an eigenvalue, while the other depends as well on the number of boundary components. We also show that on any given Riemannian surface with smooth boundary the multiplicities of Steklov eigenvalues $σ_{k}$ are uniformly bounded in $k$ .

Multiplicity of homoclinic orbits for a class of asymptotically periodic Hamiltonian systems

Piero Montecchiari (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove the existence of infinitely many geometrically distinct homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems.

Multiplicity of positive and nodal solutions for nonhomogeneous elliptic problems in unbounded cylinder domains.

Hsu, Tsing-San (2009)

Boundary Value Problems [electronic only]

Multiplicity of positive solutions for second order quasilinear equations

Dahmane Bouafia, Toufik Moussaoui, Donal O'Regan (2020)

Mathematica Bohemica

We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.

Multiplicity of positive solutions of nonlinear elliptic equations with critical sobolev exponent in some contractible domains.

Donato Passaseo (1989)

Manuscripta mathematica

Multiplicity of solutions for a class of elliptic systems in $ℝ^{N}$ .

Figueiredo, Giovany M. (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Multiplicity of solutions for gradient systems using Landesman-Lazer conditions.

da Silva, Edcarlos D. (2010)

Abstract and Applied Analysis

Multiplicity results for nonlinear elliptic equations.

Benmouloud, Samira, Khiddi, Mostafa, Sbai, Simohammed (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Multiplicity results for $p$ -sublinear $p$ -Laplacian problems involving indefinite eigenvalue problems via Morse theory.

Perera, Kanishka, Agarwal, Ravi P., O'Regan, Donal (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Multiplicity results for the prescribed scalar curvature on low spheres

Mohamed Ben Ayed, Mohameden Ould Ahmedou (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres $𝕊^{3}, 𝕊^{4}$ . Under generic conditions we establish someMorse Inequalities at Infinity, which give a lower bound on the number of solutions to the above problem in terms of the total contribution of its critical points at Infinityto the difference of topology between the level sets of the associated Euler-Lagrange functional. As a by-product of our arguments we derive a new existence...

Multisymplectic forms of degree three in dimension seven

Bureš, Jarolím, Vanžura, Jiří (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

A multisymplectic 3-structure on an $n$ -dimensional manifold $M$ is given by a closed smooth 3-form $ω$ of maximal rank on $M$ which is of the same algebraic type at each point of $M$ , i.e. they belong to the same orbit under the action of the group $G L (n, ℝ)$ . This means that for each point $x \in M$ the form $ω_{x}$ is isomorphic to a chosen canonical 3-form on $ℝ^{n}$ . R. Westwick [Linear Multilinear Algebra 10, 183–204 (1981; Zbl 0464.15001)] and D. Ž. Djoković [Linear Multilinear Algebra 13, 3–39 (1983; Zbl 0515.15011)] obtained...

Multi-time sprays and $h$ -traceless maps on $J^{1} (T, M)$ .

Neagu, Mircea, Udrişte, Constantin, Oană, Alexandru (2005)

Balkan Journal of Geometry and its Applications (BJGA)

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