PARTIAL DIFFERENTIAL EQUATIONS OF ELLIPTIC TYPE IN NONSMOOTH DOMAINS

2005 ◽  
Vol 07 (06) ◽  
pp. 787-808
Author(s):  
HELDER CANDIDO RODRIGUES
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Existence Result ◽  
Critical Case ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elliptic Type ◽  
Nonsmooth Domains ◽  
Definition Of

This paper studies the problem -Δu + λu = up in nonsmooth domains with mixed boundary conditions. Special attention will be given here to the critical case and to domains which have no further regularity than a Lipschitzian boundary. For such domains, we obtain a generalized version of Cherrier's inequality and prove an existence result. This was achieved by using an extended definition of the manifold.

scholarly journals Multiple Solutions of Second-Order Damped Impulsive Differential Equations with Mixed Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jian Liu ◽  
Lizhao Yan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Mixed Boundary ◽  
Impulsive Differential Equations ◽  
Mixed Boundary Conditions ◽  
Second Order ◽  
Multiplicity Of Solutions

We use variational methods to investigate the solutions of damped impulsive differential equations with mixed boundary conditions. The conditions for the multiplicity of solutions are established. The main results are also demonstrated with examples.

scholarly journals INTERVAL EXTENSION STRUCTURE BASIC TYPES OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER

2018 ◽  
pp. 10-14
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Interval Function ◽  
The Third ◽  
Interval Extension ◽  
The Neumann Problem

. In this article, the interval expansion of the structure of solving basic types of boundary value problems for partial differential equations of the second order of making the basic operations that compose interval arithmetic is developed. For the differential equation (1) of the type, when constructing the interval expansion of the structure of the formula, structural formulas were used to construct with the Rfunction method and 4 problems were studied — the Dirichlet problem, the Neumann problem, the third type problem, the mixed boundary conditions problem. For the Dirichlet problem, the solution is an interval expansion of the structure in the form (5), where 𝑃 = {𝜔𝛷 , 𝜔𝛷̅, 𝜔̅𝛷, 𝜔̅𝛷̅} и [ 𝛷, 𝛷̅]is an indefinite interval function. For the Neumann problem, a solution is solved in the interval extension of the structure, [ 𝛷1, 𝛷1̅̅̅̅], [ 𝛷2, 𝛷2̅̅̅̅] is an indefinite interval function and 𝐷1 is a differential operator of the form. For the problem of the third type, the solution is solved in the interval extension of the structure, [ 𝛷1, 𝛷1̅̅̅̅], [𝛷2, 𝛷2̅̅̅̅] -indefinite, interval function, 𝐷1 - differential operator of the form (9). For the problem, mixed boundary conditions are treated. The solution In the interval extension of the structure,[ 𝛷1, 𝛷1], [ 𝛷2, 𝛷2̅̅̅̅] is an indefinite interval function and 𝐷1 is a differential operator of the form.

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