Search results for "Critical points"
showing 10 items of 44 documents
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 non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian
2021
The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.
Above-bandgap ordinary optical properties of GaSe single crystal
2009
We report above-bandgap ordinary optical properties of ε-phase GaSe single crystal. Reference-quality pseudodielectric function 〈ε(E)〉 = 〈ε1(E)〉+i〈ε2(E)〉 and pseudorefractive index 〈N(E)〉 = 〈n(E)〉+i〈k(E)〉 spectra were measured by spectroscopic ellipsometry from 0.73 to 6.45 eV at room temperature for the light polarization perpendicular to the optic axis (math⊥math). The 〈ε〉 spectrum exhibited several interband-transition critical-point structures. Analysis of second-energy derivatives calculated numerically from the measured data yielded the critical-point energy values. Carmen.Martinez-Tomas@uv.es
Multiple solutions for quasilinear elliptic problems via critical points in open sublevels and truncation principles
2012
Abstract We study a quasilinear elliptic problem depending on a parameter λ of the form − Δ p u = λ f ( u ) in Ω , u = 0 on ∂ Ω . We present a novel variational approach that allows us to obtain multiplicity, regularity and a priori estimate of solutions by assuming certain growth and sign conditions on f prescribed only near zero. More precisely, we describe an interval of parameters λ for which the problem under consideration admits at least three nontrivial solutions: two extremal constant-sign solutions and one sign-changing solution. Our approach is based on an abstract localization principle of critical points of functionals of the form E = Φ − λ Ψ on open sublevels Φ − 1 ( ] − ∞ , …
Critical points of higher order for the normal map of immersions in Rd
2012
We study the critical points of the normal map v : NM -> Rk+n, where M is an immersed k-dimensional submanifold of Rk+n, NM is the normal bundle of M and v(m, u) = m + u if u is an element of NmM. Usually, the image of these critical points is called the focal set. However, in that set there is a subset where the focusing is highest, as happens in the case of curves in R-3 with the curve of the centers of spheres with contact of third order with the curve. We give a definition of r-critical points of a smooth map between manifolds, and apply it to study the 2 and 3-critical points of the normal map in general and the 2-critical points for the case k = n = 2 in detail. In the later case we a…
Infinitely many solutions for a mixed boundary value problem
2010
The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.
Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions
2019
In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.
Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids
2018
The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points,i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) atxc], towards degenerate critical points,i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood ofxcand allo…
Raman study of self-assembled InAs/InP quantum wire stacks with varying spacer thickness
2008
http://link.aip.org/link/?JAPIAU/104/033523/1
Pressure stability field of Mg-perovskite under deep mantle conditions: A topological approach based on Bader's analysis coupled with catastrophe the…
2019
Abstract The pressure stability field of the Mg-perovskite phase was investigated by characterizing the evolution of the electron arrangement in the crystal. Ab initio calculations of the perovskite structures in the range 0–185 GPa were performed at the HF/DFT (Hartree-Fock/Density Functional Theory) exchange–correlation terms level. The electron densities, calculated throughout the ab-initio wave functions, were analysed by means of the Bader's theory, coupled with Thom's catastrophe theory. To the best of our knowledge the approach is used for the first time. The topological results show the occurrence of two topological anomalies at P~20 GPa and P~110 GPa which delineate the pressure ra…