Search results for "Variational method"
showing 10 items of 46 documents
Multiple Solutions for Fractional Boundary Value Problems
2018
Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.
On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations
2016
In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.
A double mean field equation related to a curvature prescription problem
2019
We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some range of parameters. Finally, we provide existence of min-max solutions for a wider range of parameters, which is dense in the plane if $��$ is not simply connected.
Infinitely many solutions to boundary value problem for fractional differential equations
2018
Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result.
Exact and Variational Treatment of Ferroelectric Thin Films with Different Materials of Electrodes
2005
We trace the influence of metallic electrodes on the properties of thin ferroelectric films. This has been done in the framework of the phenomenological Landau theory. We present both exact analytical solution of the problem in terms of Weierstrass elliptic functions and the variational solution. We calculate polarization, dielectric susceptibility, pyroelectric coefficient and depolarization field. We have shown that the ferroelectric phase of the film can be destroyed by the choice of material of electrodes with screening length exceeding some critical value. This demonstrates that we can control the physical properties of thin ferroelectric films by the proper choice of the electrode mat…
Quantum critical point in a periodic Anderson model
2000
We investigate the symmetric Periodic Anderson Model (PAM) on a three-dimensional cubic lattice with nearest-neighbor hopping and hybridization matrix elements. Using Gutzwiller's variational method and the Hubbard-III approximation (which corresponds to the exact solution of an appropriate Falicov-Kimball model in infinite dimensions) we demonstrate the existence of a quantum critical point at zero temperature. Below a critical value $V_c$ of the hybridization (or above a critical interaction $U_c$) the system is an {\em insulator} in Gutzwiller's and a {\em semi-metal} in Hubbard's approach, whereas above $V_c$ (below $U_c$) it behaves like a metal in both approximations. These prediction…
Infinitely many solutions for a perturbed p-Laplacian boundary value problem with impulsive effects
2017
In this paper, we deal with the existence of weak solutions for a perturbed p-Laplacian boundary value problem with impulsive effects. More precisely, the existence of an exactly determined open interval of positive parameters for which the problem admits infinitely many weak solutions is established. Our proofs are based on variational methods.
Triple solutions for nonlinear elliptic problems driven by a non-homogeneous operator
2020
Abstract Some multiplicity results for a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of p -Laplacian type are given. Via variational methods, the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and/or nonlinear terms satisfying different asymptotic conditions.
Least energy solutions to the Dirichlet problem for the equation −D(u) = f (x, u)
2017
Let be a bounded smooth domain in RN. We prove a general existence result of least energy solutions and least energy nodal ones for the problem −u = f(x, u) in u = 0 on ∂ (P) where f is a Carathéodory function. Our result includes some previous results related to special cases of f . Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type f(x, u) = λ|u| s−2u − μ|u| r−2u, with s, r ∈ (1, 2) and λ,μ > 0.
CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration
2017
International audience; In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a ``twicing'' flavor a…