Geodesic
Multiplicity of positive solutions for second order quasilinear equations
Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 93-112
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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.
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.
DOI : 10.21136/MB.2019.0051-18
Classification : 30E25, 35A15, 35B38, 49K35, 58E30
Keywords: critical point; Ekeland variational principle; Mountain Pass Theorem; Palais-Smale condition; positive solution 
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Bouafia, Dahmane; Moussaoui, Toufik; O'Regan, Donal. Multiplicity of positive solutions for second order quasilinear equations. Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 93-112. doi: 10.21136/MB.2019.0051-18

[1] Alves, C. O.: Multiple positive solutions for equations involving critical Sobolev exponent in $\mathbb{R}^{N}$. Electron. J. Differ. Equ. 13 (1997), Paper No. 13, 10 pages. | MR | JFM

[2] Bouafia, D., Moussaoui, T., O'Regan, D.: Existence of solutions for a second order problem on the half-line via Ekeland's variational principle. Discuss. Math. Differ. Incl. Control Optim. 36 (2016), 131-140. | DOI | MR

[3] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2010). | DOI | MR | JFM

[4] Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47 (1974), 324-353. | DOI | MR | JFM

[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. | MR | JFM

[6] Jabri, Y.: The Mountain Pass Theorem. Variants, Generalizations and Some Applications. Encyclopedia of Mathematics and Its Applications 95. Cambridge University Press, Cambridge (2003). | DOI | MR | JFM

[7] Willem, M.: Minimax Theorems. Progress in Nonlinear Differential Equations and Their Applications 24. Birkhäuser, Boston (1996). | DOI | MR | JFM

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