Search results for "variational method"

Infinitely many weak solutions for a mixed boundary value system with (p_1,…,p_m)-Laplacian

2014

The aim of this paper is to prove the existence of infinitely many weak solu- tions for a mixed boundary value system with (p1, . . . , pm)-Laplacian. The approach is based on variational methods.

Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains

1995

Existence of two positive solutions for anisotropic nonlinear elliptic equations

2021

This paper deals with the existence of nontrivial solutions for a class of nonlinear elliptic equations driven by an anisotropic Laplacian operator. In particular, the existence of two nontrivial solutions is obtained, adapting a two critical point results to a suitable functional framework that involves the anisotropic Sobolev spaces.

Ordinary (p_1,...,p_m)-Laplacian system with mixed boundary value

2016

In this paper we prove the existence of multiple weak solutions for an ordinary mixed boundary value system with (p_1,...,p_m)-Laplacian by using recent results of critical points.

Two non-zero solutions for Sturm–Liouville equations with mixed boundary conditions

2019

Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem.

Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems

2017

We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…

Nonlinear elliptic equations with asymmetric asymptotic behavior at $pminfty$

2016

We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at $+infty$ and sublinear at $-infty$. Using minimax methods together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions one of which is negative.

Variational Bethe ansatz approach for dipolar one-dimensional bosons

2020

We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model. We apply our variational approximation to a gas of dipolar bosons in the single mode approximation and obtain its ground state energy per unit length. This allows for the calculation of the Tomonaga-Luttinger exponent as a function of density and the determination of the structure factor at small momenta. Moreover, in the case of attractive dipolar interaction, an instability is predicted at a critical density, which could be accessed in lanthanide atoms.

Existence of three solutions for a mixed boundary value system with (p_1,...,p_m)-Laplacian

2014

In this paper we prove the existence of at least three weak solutions for a mixed boundary value system with (p_1,,...,p_m)-Laplacian. The approach is based on variational methods.

On the discreet spectrum of fractional quantum hydrogen atom in two dimensions

2019

We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for $\mu>1$ (more specifically $1 < \mu \leq 2$, where $\mu=2$ corresponds to "ordinary" 2D hydrogenic problem), where $\mu$ is the L\'evy index. We show also that in fractional 2D hydrogen atom, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number $n$ but also on orbital $m$. To solve the spectral problem, we pass to the momentum representation, where we apply the variational method. This permits to obtain approximate analytica…