Multiplicity of positive solutions for second order quasilinear equations

Dahmane Bouafia; Toufik Moussaoui; Donal O'Regan

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 1, page 93-112
  • ISSN: 0862-7959

Abstract

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We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.

How to cite

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Bouafia, Dahmane, Moussaoui, Toufik, and O'Regan, Donal. "Multiplicity of positive solutions for second order quasilinear equations." Mathematica Bohemica 145.1 (2020): 93-112. <http://eudml.org/doc/297134>.

@article{Bouafia2020,
abstract = {We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.},
author = {Bouafia, Dahmane, Moussaoui, Toufik, O'Regan, Donal},
journal = {Mathematica Bohemica},
keywords = {critical point; Ekeland variational principle; Mountain Pass Theorem; Palais-Smale condition; positive solution},
language = {eng},
number = {1},
pages = {93-112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multiplicity of positive solutions for second order quasilinear equations},
url = {http://eudml.org/doc/297134},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Bouafia, Dahmane
AU - Moussaoui, Toufik
AU - O'Regan, Donal
TI - Multiplicity of positive solutions for second order quasilinear equations
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 1
SP - 93
EP - 112
AB - We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
LA - eng
KW - critical point; Ekeland variational principle; Mountain Pass Theorem; Palais-Smale condition; positive solution
UR - http://eudml.org/doc/297134
ER -

References

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  1. Alves, C. O., Multiple positive solutions for equations involving critical Sobolev exponent in ℝ N , Electron. J. Differ. Equ. 13 (1997), Paper No. 13, 10 pages. (1997) Zbl0886.35056MR1461975
  2. Bouafia, D., Moussaoui, T., O'Regan, D., 10.7151/dmdico.1187, Discuss. Math. Differ. Incl. Control Optim. 36 (2016), 131-140. (2016) MR3644383DOI10.7151/dmdico.1187
  3. Brezis, H., 10.1007/978-0-387-70914-7, Universitext. Springer, New York (2010). (2010) Zbl1220.46002MR2759829DOI10.1007/978-0-387-70914-7
  4. Ekeland, I., 10.1016/0022-247X(74)90025-0, J. Math. Anal. Appl. 47 (1974), 324-353. (1974) Zbl0286.49015MR0346619DOI10.1016/0022-247X(74)90025-0
  5. Frites, O., Moussaoui, T., O'Regan, D., Existence of solutions via variational methods for a problem with nonlinear boundary conditions on the half-line, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 22 (2015), 395-407. (2015) Zbl1333.34029MR3423280
  6. Jabri, Y., 10.1017/CBO9780511546655, Encyclopedia of Mathematics and Its Applications 95. Cambridge University Press, Cambridge (2003). (2003) Zbl1036.49001MR2012778DOI10.1017/CBO9780511546655
  7. Willem, M., 10.1007/978-1-4612-4146-1, Progress in Nonlinear Differential Equations and Their Applications 24. Birkhäuser, Boston (1996). (1996) Zbl0856.49001MR1400007DOI10.1007/978-1-4612-4146-1

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