Results 11 to 20 of about 691 (48)

On the existence of the solution of Burgers′ equation for n ≤ 4

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 645-650, 1990., 1990
In this paper a proof of the existence of the solution of Burgers′ equation for n ≤ 4 is presented. The technique used is shown to be valid for equations with more general types of nonlinearities than is present in Burgers′ equation.
Adel N. Boules
wiley   +1 more source

A variational principle for complex boundary value problems

International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 2, Page 315-318, 1988., 1988
This paper provides a variational formalism for boundary value problems which arise in certain feilds of research such as that of electricity, where the associated boundary conditions contain complex periodic conditions. A functional is provided which embodies the boundary conditions of the problem and hence the expansion (trial) functions need not ...
Adnan Atef Hajj
wiley   +1 more source

A Positive Solution for a Nonlocal Schrödinger Equation [PDF]

Bull. Aust. Math. Soc. 90 (2014) 469-475, 2014
We provide an existence result of radially symmetric, positive, classical solutions for a nonlinear Schr\"{o}dinger equation driven by the infinitesimal generator of a rotationally invariant L\'{e}vy process.
arxiv   +1 more source

Symmetry in variational principles and applications [PDF]

, 2011
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications to PDEs, fixed point theory and geometric analysis.
arxiv   +1 more source

Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb{R}^N$ [PDF]

, 2012
We construct solutions to a class of Schr\"{o}dinger equations involving the fractional laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.
arxiv   +1 more source

Perturbation results for some nonlinear equations involving fractional operators [PDF]

arXiv, 2012
By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.
arxiv  

On Symmetry of Minimizers in Constrained Quasi-Linear Problems, 1 [PDF]

arXiv, 2010
We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization ...
arxiv  

Multiple solutions of a nonlinear biharmonic equation on graphs [PDF]

arXiv, 2022
In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph. Using the variation method, we prove that the equation has two distinct solutions under certain conditions.
arxiv  

Symmetry groups and Lagrangians associated to Tzitzeica surfaces [PDF]

arXiv, 1999
One applies the symmetry group theory for study the partial differential equations of Tzitzeica surfaces theory. One finds infinitesimal symmetries, Lagrangians and a new solution of Titzeica equation.
arxiv  

Rayleigh quotients of the level set manifolds related to the nonlinear PDE [PDF]

arXiv, 2021
The main topic of this note is a discussion of applicability conditions of the Nehari manifold method depending on the value of parameters of equations. As the main tool, we apply the nonlinear generalized Rayleigh quotient method.
arxiv