Search results for "Critical point"

Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter

2013

The existence of at least one nontrivial periodic solution for a class of second order Hamiltonian systems depending on a parameter is obtained, under an algebraic condition on the nonlinearity G and without requiring any asymptotic behavior neither at zero nor at infinity. The existence is still deduced in the particular case when G is subquadratic at zero. Finally, two multiplicity results are proved if G, in addition, is required to fulfill some different Ambrosetti-Rabinowitz type superquadratic conditions at infinity. The approach is fully variational. © Heldermann Verlag.

Multiple solutions for a Sturm-Liouville problem with mixed boundary conditions

2010

Minimal unit vector fields

2002

We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.

Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian

2017

Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.

Analysis of Dissolved-Gas Atomization: Supercritical CO2 Dissolved in Water

2010

Supercritical dissolved-gas atomization is an atomization process in which carbon dioxide at temperature and pressure above its critical point is used as the atomizing gas. The spray characteristics in terms of droplets size and distribution have been experimentally studied using a laser diffraction method based on a Malvern apparatus. The main parameter that influences the droplets size is the gas-to-liquid mass ratio (GLR); the injection pressure in the range of 7.4-13 MPa has a minor effect. Upon variation of the GLR from 0.5 to 3, the droplet mean diameter changes from about 8.0 to 2.0 μm; very narrow droplet size distributions are also produced. From the point of view of the atomizatio…

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.

An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities

2005

AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.

Existence of three solutions for a quasilinear two point boundary value problem

2002

In this paper we deal with the existence of at least three classical solutions for the following ordinary Dirichlet problem:¶¶ $ \left\{\begin{array}{ll} u'' + \lambda h(u')f(t,\:u) = 0\\ u(0) = u(1) = 0.\\\end{array}\right.\ $ ¶¶Our main tool is a recent three critical points theorem of B. Ricceri ([10]).

Three solutions for a perturbed Dirichlet problem

2008

Abstract In this paper we prove the existence of at least three distinct solutions to the following perturbed Dirichlet problem: { − Δ u = f ( x , u ) + λ g ( x , u ) in  Ω u = 0 on  ∂ Ω , where Ω ⊂ R N is an open bounded set with smooth boundary ∂ Ω and λ ∈ R . Under very mild conditions on g and some assumptions on the behaviour of the potential of f at 0 and + ∞ , our result assures the existence of at least three distinct solutions to the above problem for λ small enough. Moreover such solutions belong to a ball of the space W 0 1 , 2 ( Ω ) centered in the origin and with radius not dependent on λ .

Two positive solutions for a Dirichlet problem with the (p,q)‐Laplacian

2020

The aim of this paper is to prove the existence of two solutions for a nonlinear elliptic problem involving the (p,q) -Laplacian operator. The solutions are obtained by using variational methods and critical points theorems. The positivity of the solutions is shown by applying a generalized version of the strong maximum principle.