scholarly journals A study of second order semilinear elliptic PDE involving measures

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2489-2506
Author(s):  
Ratan Giri ◽  
Debajyoti Choudhuri
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Weak Sense ◽  
Semilinear Elliptic Equation ◽  
Second Order ◽  
Elliptic Pde ◽  
Very Weak Solutions ◽  
Radon Measures ◽  
Semilinear Elliptic

The objective of this article is to study the boundary value problem for the general semilinear elliptic equation of second order involving L1 functions or Radon measures with finite total variation. The study investigates the existence and uniqueness of ?very weak? solutions to the boundary value problem for a given L1 function. However, a ?very weak? solution need not exist when an L1 function is replaced with a measure due to which the corresponding reduced limits has been found for which the problem admits a solution in a ?very weak? sense.

ON THE FIRST BOUNDARY VALUE PROBLEM FOR THE CLASS OF ELLIPTIC SYSTEMS DEGENERATING AT AN INNER POINT

2001 ◽  
Vol 6 (1) ◽  
pp. 147-155 ◽  
Author(s):  
S. Rutkauskas
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Second Order ◽  
Type Problem ◽  
Dirichlet Type ◽  
Holder Class ◽  
Uniqueness Of The Solution ◽  
Dirichlet Type Problem

The Dirichlet type problem for the weakly related elliptic systems of the second order degenerating at an inner point is discussed. Existence and uniqueness of the solution in the Holder class of the vector‐functions is proved.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEM ON TIME SCALES

2012 ◽  
Vol 23 (07) ◽  
pp. 1250070 ◽  
Author(s):  
ZHENJIE LIU
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Time Scale ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Second Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Monotone Method

This paper investigates the existence and uniqueness of solutions for singular second-order boundary value problem on time scales by using mixed monotone method. The theorems obtained are very general and complement the previous known results. When the time scale 𝕋 is chosen as ℝ or ℤ, the problem will be the corresponding continuous or discrete boundary value problem.

Fixed point results for single valued and set valued P-contractions and application to second order boundary value problems

2020 ◽  
Vol 36 (2) ◽  
pp. 205-214
Author(s):  
ISHAK ALTUN ◽  
HATICE ASLAN HANCER ◽  
ALI ERDURAN ◽  
◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Boundary Value ◽  
Uniqueness Result ◽  
Second Order ◽  
Point Boundary ◽  
Set Valued Mappings

In this paper, by considering the concept of set-valued nonlinear P-contraction which is newly introduced, we present some new fixed point theorems for set-valued mappings on complete metric space. Then by considering a single-valued case we provide an existence and uniqueness result for a kind of second order two point boundary value problem.

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