Search results for "critical points"
showing 10 items of 44 documents
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.
Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian
2004
AbstractThis paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93–104].
Multiple solutions for a discrete boundary value problem involving the p-Laplacian.
2008
Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.
On a mixed boundary value problem involving the p-Laplacian
2011
In this paper we prove the existence of infinitely many solutions for a mixed boundary value problem involving the one dimensional p-Laplacian. A result on the existence of three solutions is also established. The approach is based on multiple critical points theorems.
A sequence of positive solutions for sixth-order ordinary nonlinear differential problems
2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
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 ( ] − ∞ , …
Multiple solutions for a Sturm-Liouville problem with mixed boundary conditions
2010
Remark on a nonlocal isoperimetric problem
2017
Abstract We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian potential. We prove that regular critical sets of the functional are analytic. This optimal regularity holds also for critical sets of the Ohta–Kawasaki functional. We also prove that when the strength of the nonlocal part is small the ball is the only possible stable critical set.