Results 21 to 30 of about 179 (120)
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 We are concerned with the following nonlocal problem involving critical Sobolev exponent −a−b∫Ω∇u2dxΔu=λuq−2u+δu2u,x∈Ω,u=0,x∈∂Ω, where Ω is a smooth bounded domain in ℝ4, a, b > 0, 1 < q < 2, δ, and λ are positive parameters. We prove the existence of two positive solutions and obtain uniform estimates of extremal values for the problem.
Zhigao Shi, Xiaotao Qian, Simone Secchi
wiley +1 more source
General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics
Journal of Optimization Theory and Applications, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Le Phuoc Hai +2 more
openaire +2 more sources
Abstract and Applied Analysis, Volume 2022, Issue 1, 2022., 2022 In this paper, we establish a generalization of the Galewski‐Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global ...
Guy Degla +3 more
wiley +1 more source
Existence of Two Solutions for a Critical Elliptic Problem with Nonlocal Term in ℝ4
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we prove the existence of two positive solutions for a critical elliptic problem with nonlocal term and Sobolev exponent in dimension four.
Khadidja Sabri +4 more
wiley +1 more source
On p‐Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we deal with p‐Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial solutions.
Mohammed El Mokhtar ould El Mokhtar +1 more
wiley +1 more source
Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi-Uniform Spaces
Abstract and Applied Analysis, 2012 Some new vectorial Ekeland variational principles in cone quasi-uniform spaces are proved. Some new equivalent principles, vectorial quasivariational inclusion principle, vectorial quasi-optimization principle, vectorial quasiequilibrium principle are ...
Jiang Zhu +3 more
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Abstract and Applied Analysis, 2011 By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium ...
Wei-Shih Du
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Existence of solution for a Kirchhoff type problem involving the fractional p-Laplace operator
Electronic Journal of Qualitative Theory of Differential Equations, 2015 This paper is concerned with the existence of solutions to a Kirchhoff type problem involving the fractional $p$-Laplacian operator. We obtain the existence of solutions by Ekeland's variational principle.
Wenjing Chen, Shengbing Deng
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The Multiplicity of Nontrivial Solutions for a New px-Kirchhoff-Type Elliptic Problem
Journal of Function Spaces, 2021 In the paper, we study the existence of weak solutions for a class of new nonlocal problems involving a px-Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, we prove that the new px-Kirchhoff problem has at least two
Chang-Mu Chu, Yu-Xia Xiao
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Abstract and Applied Analysis, 2014 This paper is devoted to the stochastic optimal control problems for systems governed by forward-backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints.
Qingmeng Wei, Xinling Xiao
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