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Relevant bibliographies by topics / Ekeland''s Variational Principle

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Academic literature on the topic 'Ekeland''s Variational Principle'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Ekeland''s Variational Principle"

1

KANDILAKIS, D. A., M. MAGIROPOULOS, and N. ZOGRAPHOPOULOS. "EXISTENCE AND BIFURCATION RESULTS FOR FOURTH-ORDER ELLIPTIC EQUATIONS INVOLVING TWO CRITICAL SOBOLEV EXPONENTS." Glasgow Mathematical Journal 51, no. 1 (2009): 127–41. http://dx.doi.org/10.1017/s0017089508004588.

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AbstractLet Ω be a smooth bounded domain in RN, with N ≥ 5. We provide existence and bifurcation results for the elliptic fourth-order equation Δ2u − Δpu = f(λ, x, u) in Ω, under the Dirichlet boundary conditions u = 0 and ∇u = 0. Here λ is a positive real number, 1 < p ≤ 2# and f(.,., u) has a subcritical or a critical growth s, 1 < s ≤ 2*, where $2^{\ast}:=\frac{2N}{N-4}$ and $2^{\#}:=\frac{2N}{N-2}$. Our approach is variational, and it is based on the mountain-pass theorem, the Ekeland variational principle and the concentration-compactness principle.

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2

Aghayeva, Charkaz. "Stochastic optimal control problem of constrained switching system with delay." Filomat 30, no. 3 (2016): 711–20. http://dx.doi.org/10.2298/fil1603711a.

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This paper concerns the stochastic optimal control problem of switching systems with delay. The evolution of the system is governed by the collection of stochastic delay differential equations with initial conditions that depend on its previous state. The restriction on the system is defined by the functional constraint that contains state and time parameters. First, maximum principle for stochastic control problem of delay switching system without constraint is established. Finally, using Ekeland?s variational principle, the necessary condition of optimality for control system with constraint

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3

BENAHMED, S., and D. AZÉ. "ON FIXED POINTS OF GENERALIZED SET-VALUED CONTRACTIONS." Bulletin of the Australian Mathematical Society 81, no. 1 (2009): 16–22. http://dx.doi.org/10.1017/s000497270900046x.

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AbstractUsing a variational method introduced in [D. Azé and J.-N. Corvellec, ‘A variational method in fixed point results with inwardness conditions’, Proc. Amer. Math. Soc.134(12) (2006), 3577–3583], deriving directly from the Ekeland principle, we give a general result on the existence of a fixed point for a very general class of multifunctions, generalizing the recent results of [Y. Feng and S. Liu, ‘Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings’, J. Math. Anal. Appl.317(1) (2006), 103–112; D. Klim and D. Wardowski, ‘Fixed point theorems

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4

Pucci, Patrizia, Mingqi Xiang, and Binlin Zhang. "Existence results for Schrödinger–Choquard–Kirchhoff equations involving the fractional p-Laplacian." Advances in Calculus of Variations 12, no. 3 (2019): 253–75. http://dx.doi.org/10.1515/acv-2016-0049.

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AbstractThe paper is concerned with existence of nonnegative solutions of a Schrödinger–Choquard–Kirchhoff-type fractional p-equation. As a consequence, the results can be applied to the special case(a+b\|u\|_{s}^{p(\theta-1)})[(-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u]=\lambda f(x,u)% +\Bigg{(}\int_{\mathbb{R}^{N}}\frac{|u|^{p_{\mu,s}^{*}}}{|x-y|^{\mu}}\,dy% \Biggr{)}|u|^{p_{\mu,s}^{*}-2}u\quad\text{in }\mathbb{R}^{N},where\|u\|_{s}=\Bigg{(}\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}% \,dx\,dy+\int_{\mathbb{R}^{N}}V(x)|u|^{p}\,dx\Biggr{)}^{\frac{1}{p}},{a,b\in\mathbb{R}^{+}_{0}}, with

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5

WU, Bo. "Note on Ekeland Variational Principle." Acta Analysis Functionalis Applicata 12, no. 3 (2011): 216–20. http://dx.doi.org/10.3724/sp.j.1160.2010.00216.

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6

Suzuki, Tomonari. "The strong Ekeland variational principle." Journal of Mathematical Analysis and Applications 320, no. 2 (2006): 787–94. http://dx.doi.org/10.1016/j.jmaa.2005.08.004.

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7

Alfuraidan, Monther Rashed, and Mohamed Amine Khamsi. "Ekeland variational principle on weighted graphs." Proceedings of the American Mathematical Society 147, no. 12 (2019): 5313–21. http://dx.doi.org/10.1090/proc/14642.

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8

Mingqi, Xiang, Vicenţiu D. Rădulescu, and Binlin Zhang. "Combined effects for fractional Schrödinger–Kirchhoff systems with critical nonlinearities." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 3 (2018): 1249–73. http://dx.doi.org/10.1051/cocv/2017036.

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In this paper, we investigate the existence of solutions for critical Schrödinger–Kirchhoff type systems driven by nonlocal integro–differential operators. As a particular case, we consider the following system: [see formula in PDF] where (–Δ)sp is the fractional p–Laplace operator with 0 < s < 1 < p < N/s, α, β > 1 with α + β =p*s, M : ℝ+0 → ℝ+0 is a continuous function, V : ℝN → ℝ+ is a continuous function, λ > 0 is a real parameter. By applying the mountain pass theorem and Ekeland’s variational principle, we obtain the existence and asymptotic behaviour of solutions for t

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9

Bu, Weichun, Tianqing An, Guoju Ye, and Said Taarabti. "Negative Energy Solutions for a New Fractional p x -Kirchhoff Problem without the (AR) Condition." Journal of Function Spaces 2021 (March 22, 2021): 1–13. http://dx.doi.org/10.1155/2021/8888078.

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In this paper, we investigate the following Kirchhoff type problem involving the fractional p x -Laplacian operator. a − b ∫ Ω × Ω u x − u y p x , y / p x , y x − y N + s p x , y d x d y L u = λ u q x − 2 u + f x , u x ∈ Ω u = 0 x ∈ ∂ Ω , , where Ω is a bounded domain in ℝ N with Lipschitz boundary, a ≥ b > 0 are constants, p x , y is a function defined on Ω ¯ × Ω ¯ , s ∈ 0 , 1 , and q x > 1 , L u is the fractional p x -Laplacian operator, N > s p x , y , for any x , y ∈ Ω ¯ × Ω ¯ , p x ∗ = p x , x N / N − s p x , x , λ is a given positive parameter, and f is a continuous function. By

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10

Kim, Yun-Ho. "Existence and Multiplicity of Solutions to a Class of Fractional p-Laplacian Equations of Schrödinger-Type with Concave-Convex Nonlinearities in ℝN". Mathematics 8, № 10 (2020): 1792. http://dx.doi.org/10.3390/math8101792.

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We are concerned with the following elliptic equations: (−Δ)psv+V(x)|v|p−2v=λa(x)|v|r−2v+g(x,v)inRN, where (−Δ)ps is the fractional p-Laplacian operator with 0<s<1<r<p<+∞, sp<N, the potential function V:RN→(0,∞) is a continuous potential function, and g:RN×R→R satisfies a Carathéodory condition. By employing the mountain pass theorem and a variant of Ekeland’s variational principle as the major tools, we show that the problem above admits at least two distinct non-trivial solutions for the case of a combined effect of concave–convex nonlinearities. Moreover, we present a resu

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