Results 81 to 90 of about 838 (110)

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

arXiv, 2012
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 and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.
arxiv  

Cahn–Hilliard equation on the boundary with bulk condition of Allen–Cahn type

Advances in Nonlinear Analysis, 2018
The well-posedness of a system of partial differential equations with dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk Ω and on the boundary Γ.
Colli Pierluigi, Fukao Takeshi
doaj   +1 more source

Generalized solution of a mixed problem for linear hyperbolic system [PDF]

arXiv, 2013
In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave propagation problem in a discontinuous environment.
arxiv  

Multiplicity of Positive Solutions of P-Laplacian Systems With Sign-Changing Weight Functions [PDF]

arXiv, 2013
In this paper, we study the multiplicity of positive solutions for the p-Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.
arxiv  

Existence and non-existence of solutions to a Hamiltonian strongly degenerate elliptic system

Advances in Nonlinear Analysis, 2017
We study the non-existence and existence of infinitely many solutions to the semilinear degenerate elliptic ...
Anh Cung The, My Bui Kim
doaj   +1 more source

Approximation of elliptic equations with BMO coefficients [PDF]

arXiv, 2014
We study solution techniques for elliptic equations in divergence form, where the coefficients are only of bounded mean oscillation (BMO). For $|p-2|<\varepsilon$ and a right hand side in $W^{-1}_p$ we show convergence of a finite element scheme, where $\varepsilon$ depends on the oscillation of the coefficients.
arxiv  

On a new transformation for generalised porous medium equations: from weak solutions to classical [PDF]

arXiv, 2014
It is well-known that solutions for generalised porous medium equations are, in general, only H\"older continuous. In this note, we propose a new variable substitution for such equations which transforms weak solutions into classical.
arxiv  

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source

On the minimality of the Winterbottom shape [PDF]

arXiv
In this short note we prove that the Winterbottom shape [Winterbottom: Acta Metallurgica (1967)] is a volume-constraint minimizer of the corresponding anisotropic capillary functional.
arxiv  

Maximal $L^p-L^q$ regularity to the Stokes Problem with Navier boundary conditions [PDF]

arXiv, 2016
We prove in this paper some results on the complex and fractional powers of the Stokes operator with slip frictionless boundary conditions involving the stress tensor. This is fundamental and plays an important role in the associated parabolic problem and will be used to prove maximal $L^{p}-L^{q}$ regularity results for the non-homogeneous Stokes ...
arxiv