A note on Leighton's variational lemma for fractional Laplace equations
type: Item
instance of: scholarly article
title: A note on Leighton's variational lemma for fractional Laplace equations
zbMATH Open document ID: 1403.35110
DOI: 10.4171/ZAA/1632
author: J. Tyagi
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2018-11-15T00:00:00Z
review text: Summary: In this note, we establish Leighton's variational lemma for fractional Laplace equations. We use the classical techniques to establish this variational lemma. We also point out several questions concerning the zeros of the solutions to fractional Laplace equations which play an important role in the qualitative theory of fractional Laplace equations.
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6979891
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: Leighton's variational lemma
MaRDI profile type: Publication
Wikidata QID: Q124810890
cites work: On the discrete version of Picone's identity
cites work: Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
cites work: Comparison Theorems for Elliptic Differential Equations
cites work: Nonlocal Harnack inequalities
cites work: Hitchhiker's guide to the fractional Sobolev spaces
cites work: All functions are locally \(s\)-harmonic up to a small error
cites work: Q3435446
cites work: On the bifurcation results for fractional Laplace equations
cites work: Stability of Positive Solution to Fractional Logistic Equations
cites work: Bernstein and De Giorgi type problems: new results via a geometric approach
cites work: Q4505012
cites work: Fractional p-eigenvalues
cites work: On a Comparison Theorem for Self-Adjoint Partial Differential Equations of Elliptic Type
cites work: A generalization of leighton's variational theorem
cites work: Comparison Theorems for Linear Differential Equations of Second Order
cites work: Fractional eigenvalues
cites work: Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
cites work: The extremal solution for the fractional Laplacian
cites work: Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators
cites work: Mountain pass solutions for non-local elliptic operators
cites work: Q5584775
cites work: Sturm-Picone type theorems for second-order nonlinear differential equations
cites work: Q5502291
cites work: Generalizations of Sturm-Picone theorem for second-order nonlinear differential equations
cites work: Eigenvalue problem for fractional Kirchhoff Laplacian
full work available at URL: https://doi.org/10.4171/zaa/1632
OpenAlex ID: W2897191490
description: scientific article; zbMATH DE number 6979891