The eigenvalue problem for Hessian type operator

2021 ◽  
Author(s):  
Xinqun Mei
Keyword(s):  
Eigenvalue Problem ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Type Equation ◽  
Uniqueness Result ◽  
Type Operator

In this paper, we establish a global [Formula: see text] estimates for a Hessian type equation with homogeneous Dirichlet boundary. By the method of sub and sup solution, we get an existence and uniqueness result for the eigenvalue problem of a Hessian type operator.

scholarly journals A Uniqueness Result for a Simple Superlinear Eigenvalue Problem

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Michael Herrmann ◽  
Karsten Matthies
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Simulations ◽  
Convolution Operator ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Constitutive Laws ◽  
Parameter Family ◽  
Shape Constraint ◽  
Special Case ◽  
Nonlinear Eigenfunctions

AbstractWe study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein–Rutman arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983 ◽  
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

scholarly journals COMPACTNESS OF A NONLINEAR EIGENVALUE PROBLEM WITH A SINGULAR NONLINEARITY

2008 ◽  
Vol 10 (01) ◽  
pp. 17-45 ◽  
Author(s):  
PIERPAOLO ESPOSITO
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Morse Index ◽  
Dirichlet Boundary ◽  
Nonlinear Eigenvalue Problem ◽  
Uniqueness Result ◽  
Dirichlet Boundary Value Problem ◽  
All Solutions ◽  
Extremal Value ◽  
Nonlinear Eigenvalue

We study the Dirichlet boundary value problem [Formula: see text] on a bounded domain Ω ⊂ ℝN. For 2 ≤ N ≤ 7, we characterize compactness for solutions sequence in terms of spectral informations. As a by-product, we give an uniqueness result for λ close to 0 and λ* in the class of all solutions with finite Morse index, λ* being the extremal value associated to the nonlinear eigenvalue problem.

Monotone iterative sequences for non-local elliptic problems

2011 ◽  
Vol 22 (6) ◽  
pp. 533-552 ◽  
Author(s):  
MOHAMMED AL-REFAI ◽  
NIKOS I. KAVALLARIS ◽  
MOHAMED ALI HAJJI
Keyword(s):  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Uniqueness Result ◽  
Dirichlet Boundary Conditions ◽  
Iterative Sequence ◽  
Monotone Sequence ◽  
Monotone Iterative ◽  
Elliptic Differential Equations ◽  
Actual Solution ◽  
Non Local

In this paper we establish an existence and uniqueness result for a class of non-local elliptic differential equations with the Dirichlet boundary conditions, which, in general, do not accept a maximum principle. We introduce one monotone sequence of lower–upper pairs of solutions and prove uniform convergence of that sequence to the actual solution of the problem, which is the unique solution for some range of λ (the parameter of the problem). The convergence of the iterative sequence is tested through examples with an order of convergence greater than 1.

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1381-1400 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Integral Operator ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Formal Solution ◽  
Type Equation ◽  
Multiplier Theorem ◽  
Problem Of Time

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

scholarly journals Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

2020 ◽  
Vol 23 (2) ◽  
pp. 378-389
Author(s):  
Ferenc Izsák ◽  
Gábor Maros
Keyword(s):  
Fractional Order ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Integral Form ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Potential Operators

AbstractFractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

scholarly journals A Class of --Laplacian Type Equation with Potentials Eigenvalue Problem in

2009 ◽  
Vol 2009 (1) ◽  
pp. 185319 ◽  
Author(s):  
Mingzhu Wu ◽  
Zuodong Yang
Keyword(s):  
Eigenvalue Problem ◽  
Type Equation

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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