TY - JOUR
ID - 15677
TI - On a model of nonlinear differential equations with variable exponent by variational method
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - Shokooh, Saeid
AD - Department of Mathematics, Faculty of Sciences, Gonbad Kavous University,Gonbad Kavous, Iran
Y1 - 2020
PY - 2020
VL - 10
IS - 2
SP - 453
EP - 472
KW - Nonlinear models
KW - Sobolev space with variable exponent
KW - Variational method
DO - 10.22055/jamm.2020.31804.1784
N2 - One of the most important physical phenomena caused by surface adhesion forces is capillary property. Capillarity can be briefly explained by considering the effects of two opposing forces: adhesion, i.e. the attractive (or repulsive) force between the molecules of the liquid and those of the container; and cohesion, i.e. the attractive force between the molecules of the liquid. In this paper, we study a class of boundary value problems obtained from a capillary phenomenon modeling. Indeed, using a three critical points theorem, we will prove the existence of three weak solutions for a model of nonlinear differential equations with variable exponent. In this method which is based on the variational method, we correspond the differential equation with a nonlinear operator such that the critical points of this operator are weak solutions to the desired differential equation. As can be seen in the next section, there are two control parameters in the differential equation. We find intervals like and such that for and our problem has three bounded weak solutions in a Sobolev space with variable exponent.
UR - https://jamm.scu.ac.ir/article_15677.html
L1 - https://jamm.scu.ac.ir/article_15677_d456fd9e34627df31abe285bbfcc0acf.pdf
ER -