Certain contact metrics satisfying the Miao-Tam critical condition

Dhriti Sundar Patra; Amalendu Ghosh

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Displaying similar documents to “Certain contact metrics satisfying the Miao-Tam critical condition”

Bulk superconductivity in Type II superconductors near the second critical ﬁeld

Soren Fournais, Bernard Helffer (2010)

Journal of the European Mathematical Society

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We consider superconductors of Type II near the transition from the ‘bulk superconducting’ to the ‘surface superconducting’ state. We prove a new $L^{\infty}$ estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty [AS].

On a class of nonlocal problem involving a critical exponent

Anass Ourraoui (2015)

Communications in Mathematics

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In this work, by using the Mountain Pass Theorem, we give a result on the existence of solutions concerning a class of nonlocal $p$ -Laplacian Dirichlet problems with a critical nonlinearity and small perturbation.

Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent

Lan Zeng, Chun Lei Tang (2016)

Annales Polonici Mathematici

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We consider the following Kirchhoff type problem involving a critical nonlinearity: ⎧ $- [a + b (\int_{Ω} {| \nabla u | ² d x)}^{m} {] Δ u = f (x, u) + | u |}^{2 * - 2} u$ in Ω, ⎨ ⎩ u = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.

Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

Silvia Cingolani, Giuseppina Vannella (2001)

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

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We present critical groups estimates for a functional $f$ defined on the Banach space $W_{0}^{1, p} (Ω)$ , $Ω$ bounded domain in $R^{N}$ , $2 < p < \infty$ , associated to a quasilinear elliptic equation involving $p$ -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of $f$ in each critical point, we compute the critical groups of $f$ in each isolated critical point via Morse index.

On cusps and flat tops

Neil Dobbs (2014)

Annales de l’institut Fourier

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Non-invertible Pesin theory is developed for a class of piecewise smooth interval maps which may have unbounded derivative, but satisfy a property analogous to $C^{1 + ϵ}$ . The critical points are not required to verify a non-flatness condition, so the results are applicable to $C^{1 + ϵ}$ maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz.

Critical points via $Γ$ -convergence: general theory and applications

Jerrard, Robert L., Peter Sternberg (2009)

Journal of the European Mathematical Society

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On Kirchhoff type problems involving critical and singular nonlinearities

Chun-Yu Lei, Chang-Mu Chu, Hong-Min Suo, Chun-Lei Tang (2015)

Annales Polonici Mathematici

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In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ $- (a + b \int_{Ω} | \nabla u | ² d x) Δ u = u ⁵ + λ u^{q - 1} / {| x |}^{β}$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.

Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent

Jia-Feng Liao, Jiu Liu, Peng Zhang, Chun-Lei Tang (2016)

Annales Polonici Mathematici

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We study the following singular elliptic equation with critical exponent ⎧ $- Δ u = Q (x) u^{2 * - 1} + λ u^{- γ}$ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.

A generalization of boundedly compact metric spaces

Gerald Beer, Anna Di Concilio (1991)

Commentationes Mathematicae Universitatis Carolinae

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A metric space $〈 X, d 〉$ is called a $UC$ space provided each continuous function on $X$ into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that $UC$ spaces play relative to the compact metric spaces.

Fractal star bodies

Irmina Herburt, Maria Moszyńska, Dorette Pronk (2009)

Banach Center Publications

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In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for $L_{p}$ metrics for all p ≥ 2 and the symmetric difference metric.