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On a semilinear elliptic equation in n

Gianni Mancini, Kunnath Sandeep (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.

On a volume constrained variational problem in SBV 2 ( Ω ) : part I

Ana Cristina Barroso, José Matias (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of minimizing the energy E ( u ) : = Ω | u ( x ) | 2 d x + S u Ω 1 + | [ u ] ( x ) | d H N - 1 ( x ) among all functions u S B V 2 ( Ω ) for which two level sets { u = l i } have prescribed Lebesgue measure α i . Subject to this volume constraint the existence of minimizers for E ( · ) is proved and the asymptotic behaviour of the solutions is investigated.

On a Volume Constrained Variational Problem in SBV²(Ω): Part I

Ana Cristina Barroso, José Matias (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of minimizing the energy E ( u ) : = Ω | u ( x ) | 2 d x + S u Ω 1 + | [ u ] ( x ) | d H N - 1 ( x ) among all functions u ∈ SBV²(Ω) for which two level sets { u = l i } have prescribed Lebesgue measure α i . Subject to this volume constraint the existence of minimizers for E(.) is proved and the asymptotic behaviour of the solutions is investigated.

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

In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ - ( a + b Ω | u | ² d x ) Δ u = u + 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.

On second order Hamiltonian systems

Dana Smetanová (2006)

Archivum Mathematicum

The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.

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