四阶p-Laplacian边值问题正解的存在性

王万鹏

doi:10.13371/j.cnki.chin.q.j.m.2018.04.005

数学季刊 >

2018 , Vol. 33 >Issue 4: 377 - 385

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.04.005

四阶p-Laplacian边值问题正解的存在性

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School of Mathematics and Statistics, Huazhong University of Science and Technology

WANG Wan-peng(1994-), male(Daur), native of Qiqihar, Heilongjiang, a master of Huazhong University of Science and Technology, engages in applied mathematics.

录用日期: 2016-03-16

网络出版日期: 2020-10-07

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Existence of Positive Solutions for A Fourth-order Boundary Value Problems with p-Laplacian Operators

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School of Mathematics and Statistics, Huazhong University of Science and Technology

WANG Wan-peng(1994-), male(Daur), native of Qiqihar, Heilongjiang, a master of Huazhong University of Science and Technology, engages in applied mathematics.

Accepted date: 2016-03-16

Online published: 2020-10-07

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摘要

This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ*such that the above problem has at least two positive solutions for 0 < λ < λ* , at least one positive solution for λ = λ* and no solution forλ > λ* by using the upper and lower solutions method and fixed point theory.

关键词： Fourth-order p-Laplacian; Positive solutions; Upper and lower solutions method; Fixed point theory

本文引用格式

王万鹏 . 四阶p-Laplacian边值问题正解的存在性[J]. 数学季刊, 2018 , 33(4) : 377 -385 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.04.005

Abstract

This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem has at least two positive solutions for 0 < λ < λ~* , at least one positive solution for λ = λ~* and no solution forλ > λ~* by using the upper and lower solutions method and fixed point theory.

Key words： Fourth-order p-Laplacian; Positive solutions; Upper and lower solutions method; Fixed point theory

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