Lower and upper functions in a singular Dirichlet problem with ø-Laplacian

• Published in: Mathematical Notes Vol. 97; no. 3-4; pp. 588 - 597
• Main Authors: Rachůnková, I., Stryja, J.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-03-2015
• Subjects: Mathematics; Mathematics and Statistics; singular Dirichlet problem; time and space singularities; lower and upper functions; existence of positive solution
• ISSN: 0001-4346; 1573-8876
• DOI: 10.1134/S0001434615030293

The paper investigates the Dirichlet problem with ø-Laplacian of the form
An existence principle which can be used for problems where
f
(
t, x, y
) may have singularities at
t
= 0,
t
=
T
and also at
x
= 0,
y
= 0, is proved here. As an application of this principle, new conditions that guarantee the solvability of the above problem are found.