# The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian

• Volume: 008, Issue: 2, page 375-388
• ISSN: 1435-9855

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## Abstract

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We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation $\left(|{u}^{\text{'}}{|}^{p-2}{u}^{\text{'}}{\right)\right)}^{\text{'}}+f\left(u\right){u}^{\text{'}}+g\left(x,u\right)=t$, when $f$ is arbitrary and $g\left(x,u\right)\to +\infty$ or $g\left(x,u\right)\to -\infty$ when $|u|\to \infty$. The proof uses upper and lower solutions and the Leray–Schauder degree.

## How to cite

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Mawhin, Jean. "The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian." Journal of the European Mathematical Society 008.2 (2006): 375-388. <http://eudml.org/doc/277461>.

@article{Mawhin2006,
abstract = {We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation $(|u^\{\prime \}|^\{p−2\}u^\{\prime \}))^\{\prime \}+ f(u)u^\{\prime \}+g(x,u)=t$, when $f$ is arbitrary and $g(x,u)\rightarrow +\infty$ or $g(x,u)\rightarrow −\infty$ when $|u|\rightarrow \infty$. The proof uses upper and lower solutions and the Leray–Schauder degree.},
author = {Mawhin, Jean},
journal = {Journal of the European Mathematical Society},
keywords = {Ambrosetti-Prodi problem; periodic solutions; upper and lower solutions; topological degree; Ambrosetti-Prodi problem; Periodic solutions; upper and lower solutions},
language = {eng},
number = {2},
pages = {375-388},
publisher = {European Mathematical Society Publishing House},
title = {The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian},
url = {http://eudml.org/doc/277461},
volume = {008},
year = {2006},
}

TY - JOUR
AU - Mawhin, Jean
TI - The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian
JO - Journal of the European Mathematical Society
PY - 2006
PB - European Mathematical Society Publishing House
VL - 008
IS - 2
SP - 375
EP - 388
AB - We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation $(|u^{\prime }|^{p−2}u^{\prime }))^{\prime }+ f(u)u^{\prime }+g(x,u)=t$, when $f$ is arbitrary and $g(x,u)\rightarrow +\infty$ or $g(x,u)\rightarrow −\infty$ when $|u|\rightarrow \infty$. The proof uses upper and lower solutions and the Leray–Schauder degree.
LA - eng
KW - Ambrosetti-Prodi problem; periodic solutions; upper and lower solutions; topological degree; Ambrosetti-Prodi problem; Periodic solutions; upper and lower solutions
UR - http://eudml.org/doc/277461
ER -

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