A double-phase eigenvalue problem with large exponents
Open Mathematics, 2023 In the present article, we consider a double-phase eigenvalue problem with large exponents. Let λ(pn,qn)1{\lambda }_{\left({p}_{n},{q}_{n})}^{1} be the first eigenvalues and un{u}_{n} be the first eigenfunctions, normalized by ‖un‖ℋn=1\Vert {u}_{n}{\Vert
Yu Lujuan
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Principal eigenvalue problem for infinity Laplacian in metric spaces
Advanced Nonlinear Studies, 2022 This article is concerned with the Dirichlet eigenvalue problem associated with the ∞\infty -Laplacian in metric spaces. We establish a direct partial differential equation approach to find the principal eigenvalue and eigenfunctions in a proper geodesic
Liu Qing, Mitsuishi Ayato
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Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
Advances in Nonlinear Analysis, 2022 We consider density solutions for gradient flow equations of the form ut = ∇ · (γ(u)∇ N(u)), where N is the Newtonian repulsive potential in the whole space ℝd with the nonlinear convex mobility γ(u) = uα, and α > 1.
Carrillo J.A. +2 more
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Asymptotic mean-value formulas for solutions of general second-order elliptic equations
Advanced Nonlinear Studies, 2022 We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and ...
Blanc Pablo +3 more
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Perturbed eigenvalue problems: an overview
, 2021 The study of perturbed eigenvalue problems has been a very active field of investigation throughout the years. In this survey we collect several results in the field.
MIHĂILESCU, Mihai +3 more
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Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation
Open Mathematics, 2020 In this paper, we investigate the problem for optimal control of a viscous generalized θ\theta -type dispersive equation (VG θ\theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation.
Fan Guobing, Yang Zhifeng
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Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations
Advanced Nonlinear Studies, 2020 In this paper, we study the Cauchy problem of the parabolic Monge–Ampère ...
Dai Limei, Bao Jiguang
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An improvement of level set equations via approximation of a distance function [PDF]
, 2018 In the classical level set method, the slope of solutions can be very small or large, and it can make it difficult to get the precise level set numerically.
Hamamuki, Nao
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Parabolic Biased Infinity Laplacian Equation Related to the Biased Tug-of-War
Advanced Nonlinear Studies, 2019 In this paper, we study the parabolic inhomogeneous β-biased infinity Laplacian equation arising from the β-biased tug-of ...
Liu Fang, Jiang Feida
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On viscosity and weak solutions for non-homogeneous p-Laplace equations
Advances in Nonlinear Analysis, 2017 In this manuscript, we study the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower-order term depending on x, u and ∇u{\nabla u}.
Medina Maria, Ochoa Pablo
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