Two classes of Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of a class of \(p\)-Laplacian equations

DOI10.1016/J.CAM.2018.04.020zbMath1393.35064OpenAlexW2802482572MaRDI QIDQ1639566

Xudong Yao

Publication date: 13 June 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.04.020

zbMATH Keywords

finite element methodLjusternik-Schnirelman theory\(p\)-Laplacianquasilinear equation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (5)

A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems. I. Algorithm and global convergence ⋮ A minimax algorithm based on Newton's method and an application for finding multiple solutions of p‐area problems ⋮ A Morse index formula for minimax type saddle points by a Ljusternik-Schnirelman minimax algorithm and its application in computation of multiple solutions of semilinear elliptic equation ⋮ A new augmented singular transform and its partial Newton-correction method for finding more solutions to nonvariational quasilinear elliptic PDEs ⋮ A local min-orthogonal based numerical method for computing multiple coexisting solutions to cooperative \(p\)-Laplacian systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of semilinear elliptic Dirichlet problem involving concave and convex nonlinearities. I: Algorithms and convergence
• A minimax method for finding saddle points of upper semi-differentiable locally Lipschitz continuous functional in Banach space and its convergence
• Finite element error estimates for nonlinear elliptic equations of monotone type
• Finite element methods (Part 1)
• Combined effects of concave and convex nonlinearities in some elliptic problems
• Convergence analysis of a minimax method for finding multiple solutions of semilinear elliptic equation.: I: On polyhedral domain
• Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space
• A local minimax characterization for computing multiple nonsmooth saddle critical points
• A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs
• Unified Convergence Results on a Minimax Algorithm for Finding Multiple Critical Points in Banach Spaces
• Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases
• Numerical Methods for Computing Nonlinear Eigenpairs: Part II. Non-Iso-Homogeneous Cases
• A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
• Convergence Results of a Local Minimax Method for Finding Multiple Critical Points
• A mountain pass method for the numerical solution of semilinear elliptic problems
• A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE
• A minimax method for finding saddle critical points of upper semi-differentiable locally Lipschitz continuous functional in Hilbert space and its convergence

This page was built for publication: Two classes of Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of a class of \(p\)-Laplacian equations