Author:
Cupini Giovanni,Marcelli Cristina,Papalini Francesca
Abstract
Abstract
We investigate the existence of heteroclinic solutions to a class of nonlinear differential equations
(
a
(
x
)
Φ
(
x
′
(
t
)
)
)
′
=
f
(
t
,
x
(
t
)
,
x
′
(
t
)
)
,
a
.
e
.
t
∈
ℝ
governed by a nonlinear differential operator Φ extending the classical p- Laplacian, with right-hand side f having the critical rate of decay -1 as |t| → +∞, that is
f
(
t
,
⋅
,
⋅
)
≈
1
t
. We prove general existence and non-existence results, as well as some simple criteria useful for right-hand side having the product structure f(t, x, x') = b(t, x)c(x, x').
Mathematical subject classification: Primary: 34B40; 34C37; Secondary: 34B15; 34L30.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference13 articles.
1. Bereanu C, Jebelean P, Mawhin J: Periodic solutions of pendulum-like perturbations of singular and bounded ϕ -Laplacians. J Dyn Diff Equ 2010, 22: 463-471. 10.1007/s10884-010-9172-3
2. Bereanu C, Mawhin J: Nonlinear Neumann boundary-value problems with Φ-Laplacian operators. An Stiint Univ Ovidius Constanta 2004, 12: 73-92.
3. Bereanu C, Mawhin J: Boundary-value problems with non-surjective Φ-Laplacian and one-side bounded nonlinearity. Adv Differ Equ 2006, 11: 35-60.
4. Bereanu C, Mawhin J: Existence and multiplicity results for some nonlinear problems with singular Φ-Laplacian. J Differ Equ 2007, 243: 536-557. 10.1016/j.jde.2007.05.014
5. Bereanu C, Mawhin J: Periodic solutions of nonlinear perturbations of Φ-Laplacians with possibly bounded Φ. Nonlinear Anal 2008, 68: 1668-1681.
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