Nontrivial solutions for an asymptotically linear ∆α-Laplace equation

Jiafa Xu; Jia Chen; Donal O’regan

doi:10.15388/namc.2023.28.32177

Nontrivial solutions for an asymptotically linear ∆_α-Laplace equation

Jiafa Xu
, Jia Chen
, Donal O’regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties of eigenvalues and eigenfunctions for the strongly degenerate elliptic operator and then obtain two existence theorems of nontrivial solutions when the nonlinearity is a function with an asymptotically condition.

Original language	English
Pages (from-to)	841-858
Number of pages	18
Journal	Nonlinear Analysis: Modelling and Control
Volume	28
Issue number	5
DOIs	https://doi.org/10.15388/namc.2023.28.32177
Publication status	Published - 1 Sep 2023

Keywords

asymptotically linear
saddle point theorem
strongly degenerate elliptic operator

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10.15388/namc.2023.28.32177

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title = "Nontrivial solutions for an asymptotically linear ∆α-Laplace equation",

abstract = "In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties of eigenvalues and eigenfunctions for the strongly degenerate elliptic operator and then obtain two existence theorems of nontrivial solutions when the nonlinearity is a function with an asymptotically condition.",

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AU - Xu, Jiafa

AU - Chen, Jia

AU - O’regan, Donal

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Y1 - 2023/9/1

N2 - In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties of eigenvalues and eigenfunctions for the strongly degenerate elliptic operator and then obtain two existence theorems of nontrivial solutions when the nonlinearity is a function with an asymptotically condition.

AB - In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties of eigenvalues and eigenfunctions for the strongly degenerate elliptic operator and then obtain two existence theorems of nontrivial solutions when the nonlinearity is a function with an asymptotically condition.

KW - asymptotically linear

KW - saddle point theorem

KW - strongly degenerate elliptic operator

UR - https://www.scopus.com/pages/publications/85171457587

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DO - 10.15388/namc.2023.28.32177

M3 - Article

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JO - Nonlinear Analysis: Modelling and Control

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IS - 5

ER -

Nontrivial solutions for an asymptotically linear ∆_α-Laplace equation

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