All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 68

Showing per page

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 infinitely many weak solutions for some quasilinear $\vec {p}(x)$-elliptic Neumann problems

Ahmed Ahmed, Taghi Ahmedatt, Hassane Hjiaj, Abdelfattah Touzani (2017)

Mathematica Bohemica

We consider the following quasilinear Neumann boundary-value problem of the type $$ \begin {cases} -\displaystyle \sum _{i=1}^{N}\frac {\partial }{\partial x_{i}}a_{i}\Big (x,\frac {\partial u}{\partial x_{i}}\Big ) + b(x)|u|^{p_{0}(x)-2}u = f(x,u)+ g(x,u) &\text {in} \ \Omega , \\ \quad \dfrac {\partial u}{\partial \gamma } = 0 &\text {on} \ \partial \Omega . \end {cases} $$ We prove the existence of infinitely many weak solutions for our equation in the anisotropic variable exponent Sobolev...

Existence of solutions for a class of Kirchhoff type problems in Orlicz-Sobolev spaces

Nguyen Thanh Chung (2015)

Annales Polonici Mathematici

We consider Kirchhoff type problems of the form ⎧ -M(ρ(u))(div(a(|∇u|)∇u) - a(|u|)u) = K(x)f(u) in Ω ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω where Ω ⊂ ℝ N , N ≥ 3, is a smooth bounded domain, ν is the outward unit normal to ∂Ω, ρ ( u ) = ∫ Ω ( Φ ( | ∇ u | ) + Φ ( | u | ) ) d x , M: [0,∞) → ℝ is a continuous function, K ∈ L ∞ ( Ω ) , and f: ℝ → ℝ is a continuous function not satisfying the Ambrosetti-Rabinowitz type condition. Using variational methods, we obtain some existence and multiplicity results.

Currently displaying 41 – 60 of 68