Results 51 to 60 of about 1,368 (124)
Advances in Nonlinear Analysis, 2022 This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: (P)(−Δ)su+λu=μ∣u∣p−2u+∣u∣2s∗−2u,x∈RN,u>0,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}{\left(-\Delta )}^{s}u+\lambda
Li Quanqing, Zou Wenming
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Mañé's conjectures in codimension one [PDF]
Communications on Pure and Applied Mathematics, Volume 64, Issue 7
(2011) Pages 1008-1027, 2010 We prove Ma\~n\'e's conjectures in the context of codimension one Aubry-Mather ...
arxiv +1 more source
Variational Formulation for Guided and Leaky Modes in Multilayer Dielectric Waveguides
, 2009 The guided and leaky modes of a planar dielectric waveguide are eigensolutions of a singular Sturm-Liouville problem. The modes are the roots of a characteristic function which can be found with several methods that have been introduced in the past ...
David O. Stowell, J. Tausch
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On quasilinear elliptic equations in ℝN
Abstract and Applied Analysis, Volume 1, Issue 4, Page 407-415, 1996., 1996 In this note we give a result for the operator p‐Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −Δu = h(x)uq in ℝN, where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the ...
C. O. Alves, J. V. Concalves, L. A. Maia
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Nonlocal eigenvalue problems with variable exponent
Moroccan Journal of Pure and Applied Analysis, 2018 We consider the nonlocal eigenvalue problem of the following ...
Azroul Elhoussine, Shimi Mohammed
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EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NONLINEAR SCHRÖDINGER-KIRCHHOFF-TYPE EQUATIONS
, 2016 . In this paper, we consider the following Schro¨dinger-Kirch-hoff-type equationsa+ bZ R N (|∇u| 2 + V(x)|u| 2 )dx[−∆u+ V(x)u] = f(x,u), in R N .Under certain assumptions on V and f, some new criteria on the exis-tence and multiplicity of nontrivial ...
Haibo Chen, Hongliang Liu, Liping Xu
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A weighted Hardy-type inequality for 0
, 2015 Hardy-type inequalities with sharp costants for 0 < p < 1 for power weight functions were established in [10], [5]. In this work, we give an extension of these inequalities for general weight functions, prove the existence of extremal functions and write
N. Azzouz, V. Burenkov, A. Senouci
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One‐sided resonance for quasilinear problems with asymmetric nonlinearities
, 2002 Abstract and Applied Analysis, Volume 7, Issue 1, Page 53-60, 2002.
Kanishka Perera
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On certain nonlinear elliptic systems with indefinite terms
Electronic Journal of Differential Equations, 2002 We consider an elliptic quasi linear systems with indefinite term on a bounded domain. Under suitable conditions, existence and positivity results for solutions are given. Submitted April 2, 2002. Published October 2, 2002.
Ahmed Bensedik, Mohammed Bouchekif
doaj
Existence of solutions of elliptic boundary value problems with mixed type nonlinearities
, 2012 We study the existence of a nontrivial solution of the following elliptic boundary value problem with mixed type nonlinearities: {−△u=f(x,u)in Ω,u=0on ∂Ω, where f(x,u)=−Ku+Wu. We consider the problem in a different case: lim|u|→∞f(x,u)/u=∞, lim|u|→0f(x,
Anmin Mao, Yan Zhu, S. Luan
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