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

DOI10.1007/S10915-015-0010-YzbMath1342.35032OpenAlexW2063205365MaRDI QIDQ283281

Xudong Yao

Publication date: 13 May 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-015-0010-y

zbMATH Keywords

convergencefinite element methodsemilinear elliptic equationconcave and convex nonlinearitiesLjusternik-Schnirelman critical point theoryLjusternik-Schnirelman minimax algorithm

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) 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) Variational principles in infinite-dimensional spaces (58E30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Semilinear elliptic equations (35J61) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (3)

A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems. I. Algorithm and global convergence ⋮ Two classes of Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of a class of \(p\)-Laplacian equations ⋮ 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

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