Eigenvalues of the p(x)-biharmonic operator with indefinite weight

2014 ◽  
Vol 66 (3) ◽  
pp. 1007-1021 ◽  
Author(s):  
Bin Ge ◽  
Qing-Mei Zhou ◽  
Yu-Hu Wu
Keyword(s):  
Biharmonic Operator ◽  
Indefinite Weight

scholarly journals Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions

2018 ◽  
Vol 36 (1) ◽  
pp. 195 ◽  
Author(s):  
Zakaria El Allali ◽  
Said Taarabti ◽  
Khalil Ben Haddouch
Keyword(s):  
Boundary Conditions ◽  
Neumann Boundary ◽  
Continuous Functions ◽  
Neumann Boundary Conditions ◽  
Continuous Family ◽  
Biharmonic Operator ◽  
Indefinite Weight ◽  
Positive Real ◽  
Smooth Bounded Domain ◽  
Indefinite Weight Function

In this paper we will study the existence of solutions for the nonhomogeneous elliptic equation with variable exponent $\Delta^2_{p(x)} u=\lambda V(x) |u|^{q(x)-2} u$, in a smooth bounded domain,under Neumann boundary conditions, where $\lambda$ is a positive real number, $p,q: \overline{\Omega} \rightarrow \mathbb{R}$, are continuous functions, and $V$ is an indefinite weight function. Considering different situations concerning the growth rates involved in the above quoted problem, we will prove the existence of a continuous family of eigenvalues.

scholarly journals Strict monotonicity and unique continuation of the biharmonic operator - doi: 10.5269/bspm.v30i2.14502

1970 ◽  
Vol 30 (2) ◽  
pp. 79-83
Author(s):  
Najib Tsouli ◽  
Omar Chakrone ◽  
Mostafa Rahmani ◽  
Omar Darhouche
Keyword(s):  
Unique Continuation ◽  
Biharmonic Operator ◽  
Strict Monotonicity ◽  
Unique Continuation Property ◽  
Continuation Property

In this paper, we will show that the strict monotonicity of the eigenvalues of the biharmonic operator holds if and only if some unique continuation property is satisfied by the corresponding eigenfunctions.

Spectrum theory of second-order difference equations with indefinite weight

2018 ◽  
Vol 8 (3) ◽  
pp. 971-985
Author(s):  
Ruyun Ma ◽  
Chenghua Gao ◽  
Yanqiong Lu
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Indefinite Weight ◽  
Order Difference

Sturm-Liouville operators with an indefinite weight function

1977 ◽  
Vol 78 (1-2) ◽  
pp. 161-191 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Weight Function ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Scalar Product ◽  
Main Tool ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Sturm Liouville ◽  
Liouville Operators

SynopsisSpectral properties of the singular Sturm-Liouville equation –(p−1y′)′ + qy = λry with an indefinite weight function r are studied in . The main tool is the theory of definitisable operators in spaces with an indefinite scalar product.

scholarly journals One-dimensional p-Laplacian with a strong singular indefinite weight, I. Eigenvalue

2008 ◽  
Vol 244 (8) ◽  
pp. 1985-2019 ◽  
Author(s):  
Ryuji Kajikiya ◽  
Yong-Hoon Lee ◽  
Inbo Sim
Keyword(s):  
Indefinite Weight ◽  
One Dimensional

scholarly journals Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

2020 ◽  
Vol 6 (2) ◽  
pp. 198-209
Author(s):  
Mohamed Laghzal ◽  
Abdelouahed El Khalil ◽  
My Driss Morchid Alaoui ◽  
Abdelfattah Touzani
Keyword(s):  
Dirichlet Problem ◽  
Variational Approach ◽  
Type Inequality ◽  
Biharmonic Operator ◽  
Nondecreasing Sequence ◽  
Hardy Type Inequality ◽  
Principal Curve ◽  
Hardy Type ◽  
Homogeneous Dirichlet Problem

AbstractThis paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ1(λ) and also show that, the smallest curve μ1(λ) is positive for all 0 ≤ λ < CH, with CH is the optimal constant of Hardy type inequality.

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