scholarly journals Dirichlet boundary value problem related to the p(x)-Laplacian with discontinuous nonlinearity

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 243-253
Author(s):  
Mustapha Ait Hammou ◽  
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Growth Conditions ◽  
Dirichlet Boundary Value Problem ◽  
Discontinuous Nonlinearity ◽  
Hammerstein Equation ◽  
The Right

In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to a certain p(x)-Laplacian, by using the degree theory after turning the problem into a Hammerstein equation. The right hand side is a possibly discontinuous function in the second variable satisfying some non-standard growth conditions.

Existence and Multiplicity of Positive Solutions for a Dirichlet Boundary Value Problem in ℝ2

2002 ◽  
Vol 2 (3) ◽  
Author(s):  
V. Barutello ◽  
A. Capietto ◽  
P. Habets
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Parameter Dependent ◽  
Vector Differential Equation

AbstractWe deal with the Dirichlet boundary value problem associated to a parameter-dependent second order vector differential equation. Using the method of lower and upper solutions together with degree theory, we provide existence and multiplicity of positive solutions.

scholarly journals Weak Solutions for a Second Order Dirichlet Boundary Value Problem on Time Scale

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Wandong Lou
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Existence Theorems ◽  
Boundary Value ◽  
Degree Theory ◽  
Point Theory ◽  
Second Order ◽  
Dirichlet Boundary Value Problem

We adopt the Leray-Schauder degree theory and critical point theory to consider a second order Dirichlet boundary value problem on time scales and obtain some existence theorems of weak solutions for the previous problem.

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