Positive decaying solutions for differential equations with phi-Laplacian

• Published in: Boundary value problems Vol. 2015; no. 1
• Main Authors: Došlá, Zuzana, Marini, Mauro
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 12-06-2015
• Subjects: Analysis; Approximations and Expansions; Difference and Functional Equations; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; 34B15; decaying solution; nonlinear boundary value problem; 34B40; globally positive solution; oscillatory solution; 34B18
• ISSN: 1687-2770; 1687-2770
• DOI: 10.1186/s13661-015-0355-z

We solve a nonlocal boundary value problem on the half-close interval
[
1
,
∞
)
associated to the differential equation
(
a
(
t
)
|
x
′
|
α
sgn
x
′
)
′
+
b
(
t
)
|
x
|
β
sgn
x
=
0
, in the superlinear case
α
<
β
. By using a new approach, based on a special energy-type function
E
, the existence of slowly decaying solutions is examined too.