On degenerate boundary value problems for elliptic differential operators of second order in the plane and the index of degenerate pseudo-differential operators on a closed curve

1981 ◽  
Vol 102 (1) ◽  
pp. 277-292 ◽  
Author(s):  
Johannes Elschner
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Second Order ◽  
Closed Curve ◽  
Pseudo Differential Operators ◽  
Elliptic Differential Operators

Non-well-ordered lower and upper solutions for semilinear systems of PDEs

2021 ◽  
pp. 2150080
Author(s):  
Alessandro Fonda ◽  
Giuliano Klun ◽  
Andrea Sfecci
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Parabolic Type ◽  
Existence Results ◽  
Second Order ◽  
Lower And Upper Solutions ◽  
Semilinear Systems ◽  
Systems Of Pdes ◽  
Abstract Framework

We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.

scholarly journals To the theory of discrete boundary value problems

4open ◽  
2019 ◽  
Vol 2 ◽  
pp. 17 ◽  
Author(s):  
Oksana A. Tarasova ◽  
Vladimir B. Vasilyev
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Differential Operators ◽  
Boundary Value ◽  
Continuous Solutions ◽  
Existence And Uniqueness Results ◽  
Discrete Equations ◽  
Uniqueness Results ◽  
Pseudo Differential Operators ◽  
Discrete Analogues

We consider discrete analogues of pseudo-differential operators and related discrete equations and boundary value problems. Existence and uniqueness results for special elliptic discrete boundary value problem and comparison for discrete and continuous solutions are given for certain smooth data in discrete Sobolev–Slobodetskii spaces.

scholarly journals GREEN'S FUNCTIONS AND REGULARIZED TRACES OF STURM–LIOUVILLE OPERATORS ON GRAPHS

2008 ◽  
Vol 51 (2) ◽  
pp. 315-335 ◽  
Author(s):  
Sonja Currie ◽  
Bruce A. Watson
Keyword(s):  
Boundary Value Problems ◽  
Green's Functions ◽  
Differential Operators ◽  
Green’S Functions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value ◽  
Elliptic Differential Operators ◽  
Sturm Liouville ◽  
Inverse Spectral

AbstractAsymptotic approximations to the Green's functions of Sturm–Liouville boundary-value problems on graphs are obtained. These approximations are used to study the regularized traces of the differential operators associated with these boundary-value problems. Various inverse spectral problems for Sturm–Liouville boundary-value problems on graphs resembling those considered in Halberg and Kramer's ‘A generalization of the trace concept' (Duke Mathematics Journal27 (1960), 607–617), for Sturm–Liouville problems, and Pielichowski's ‘An inverse spectral problem for linear elliptic differential operators' (Universitatis Iagellonicae Acta Mathematica27 (1988), 239–246), for elliptic boundary-value problems, are solved.

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