Bifurcation Analysis of a Class of Polyharmonic Semilinear Equations with Perturbed Potential

被引：0

作者：

Abid, Imed ^{[1
]}

Baraket, Sami ^{[2
]}

机构：

[1] Univ Tunis El Manar, Higher Inst Med Technol Tunis, Tunis, Tunisia

[2] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh 11623, Saudi Arabia

来源：

ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES | 2024年 / 51卷 / 02期

关键词：

polyharmonic equation; bifurcation; regularity; stability; quasilinear; CRITICAL DIMENSIONS; POSITIVE SOLUTIONS; CRITICAL EXPONENTS;

D O I：

10.52846/ami.v51i2.1878

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper focuses on the investigation of bifurcation phenomena in a polyharmonic semilinear problem, considering both the Dirichlet and Navier boundary conditions. We explore the existence and uniqueness of positive solutions, as well as the presence of critical values and the uniqueness of extremal solutions. Additionally, we address various bifurcation scenarios that arise in a class of elliptic problems, and we establish the asymptotic behavior of the solution in the vicinity of the bifurcation point.

引用

页码：449 / 467

页数：19

共 17 条

[1] Weak solutions of quasilinear biharmonic problems with positive, increasing and convex nonlinearities
Abid, I.
Jleli, M.
Trabelsi, N.
[J]. ANALYSIS AND APPLICATIONS, 2008, 6 (03) : 213 - 227
[2] BIFURCATION PROBLEM FOR A CLASS OF QUASILINEAR FRACTIONAL SCHRODINGER EQUATIONS
Abid, Imed
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 57 (06) : 1347 - 1372
[3] ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1.
AGMON, S
DOUGLIS, A
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1959, 12 (04) : 623 - 727
[4] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[5] [Anonymous], 1960, Bull. Amer. Math. Soc., DOI [DOI 10.1090/S0002-9904-1960-10402-8, 10.1090/S0002-9904-1960-10402-8]
[6] Berchio E, 2005, ELECTRON J DIFFER EQ
[7] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
BREZIS, H
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) : 437 - 477
[8] Brezis H., 1992, ANAL FONCTIONNELLE T
[9] CRITICAL EXPONENTS, CRITICAL DIMENSIONS AND THE BIHARMONIC OPERATOR
EDMUNDS, DE
FORTUNATO, D
JANNELLI, E
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1990, 112 (03) : 269 - 289
[10] Models of Higher Order
Gazzola, Filippo
Grunau, Hans-Christoph
Sweers, Guido
[J]. POLYHARMONIC BOUNDARY VALUE PROBLEMS: POSITIVITY PRESERVING AND NONLINEAR HIGHER ORDER ELLIPTIC EQUATIONS IN BOUNDED DOMAINS, 2010, 1991 : 1 - +

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