Page 1 Next

Displaying 1 – 20 of 21

Showing per page

Evolution Problems and Minimizing Movements

Ugo Gianazza, Massimo Gobbino, Giuseppe Savarè (1994)

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

We recall the definition of Minimizing Movements, suggested by E. De Giorgi, and we consider some applications to evolution problems. With regards to ordinary differential equations, we prove in particular a generalization of maximal slope curves theory to arbitrary metric spaces. On the other hand we present a unifying framework in which some recent conjectures about partial differential equations can be treated and solved. At the end we consider some open problems.

Existence and multiplicity of solutions for a fractional p -Laplacian problem of Kirchhoff type via Krasnoselskii’s genus

Ghania Benhamida, Toufik Moussaoui (2018)

Mathematica Bohemica

We use the genus theory to prove the existence and multiplicity of solutions for the fractional p -Kirchhoff problem - M Q | u ( x ) - u ( y ) | p | x - y | N + p s d x d y p - 1 ( - Δ ) p s u = λ h ( x , u ) in Ω , u = 0 on N Ω , where Ω is an open bounded smooth domain of N , p > 1 , N > p s with s ( 0 , 1 ) fixed, Q = 2 N ( C Ω × C Ω ) , λ > 0 is a numerical parameter, M and h are continuous functions.

Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

Sylwia Barnaś (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.

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

We consider the following Kirchhoff type problem involving a critical nonlinearity: ⎧ - [ a + b ( Ω | u | ² d x ) m ] Δ u = f ( x , u ) + | u | 2 * - 2 u in Ω, ⎨ ⎩ u = 0 on ∂Ω, where Ω 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.

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

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 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.

Currently displaying 1 – 20 of 21

Page 1 Next