Positive solutions for a semipositone problem involving nonlocal operator
Afrouzi, G. A. ; Chung, N. T. ; Shakeri, S.
Rendiconti del Seminario Matematico della Università di Padova, Tome 132 (2014), p. 25-32 / Harvested from Numdam
Access to full text
Publié le : 2014-01-01
@article{RSMUP_2014__132__25_0,
     author = {Afrouzi, G. A. and Chung, N. T. and Shakeri, S.},
     title = {Positive solutions for a semipositone problem involving nonlocal operator},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {132},
     year = {2014},
     pages = {25-32},
     mrnumber = {3276823},
     zbl = {1304.35276},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2014__132__25_0}
}

Afrouzi, G. A.; Chung, N. T.; Shakeri, S. Positive solutions for a semipositone problem involving nonlocal operator. Rendiconti del Seminario Matematico della Università di Padova, Tome 132 (2014) pp. 25-32. http://gdmltest.u-ga.fr/item/RSMUP_2014__132__25_0/

[1] G.A. Afrouzi - N.T. Chung - S. Shakeri, Existence of positive solutions for Kirchhoff type equations, Electron. J. Differential Equations 2013, no. 180, 8 pp. | MR 3091754 | Zbl 06283885

[2] C.O. Alves - F.J.S.A. Corrêa - T.M. Ma, Positive solutions for a quasilinear elliptic equation of Kirchhoff type, Comput. Math. Appl. 49 (2005), pp. 85–93. | MR 2123187 | Zbl 1130.35045

[3] A. Bensedik - M. Bouchekif, On an elliptic equation of Kirchhoff-type with a potential asymptotically linear at infinity, Math. Comput. Modelling 49 (2009), pp. 1089–1096. | MR 2495022 | Zbl 1165.35364

[4] M. Chipot - B. Lovat, Some remarks on nonlocal elliptic and parabolic problems, Nonlinear Anal. 30 (1997), no. 7, pp. 4619–4627. | MR 1603446 | Zbl 0894.35119

[5] F.J.S.A. Corrêa - G.M. Figueiredo, On an elliptic equation of p -Kirchhoff type via variational methods, Bull. Austral. Math. Soc. 74 (2006), pp. 263–277. | MR 2260494 | Zbl 1108.45005

[6] G. Dai, Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x) -Laplacian, Appl. Anal. 92 (2013), no. 1, pp. 191–210. | MR 3007931 | Zbl 1302.35169

[7] G. Dai - R. Ma, Solutions for a p(x) -Kirchhoff type equation with Neumann boundary data, Nonlinear Anal. Real World Appl. 12 (2011), pp. 2666–2680. | MR 2813212 | Zbl 1225.35079

[8] X. Han - G. Dai, On the sub-supersolution method for p(x) -Kirchhoff type equations, J. Inequal. Appl. (2012), 11 pp. | MR 3017321 | Zbl 1284.35175

[9] G. Kirchhoff, Mechanik, Teubner, Leipzig, Germany, 1883.

[10] T.F. Ma, Remarks on an elliptic equation of Kirchhoff type, Nonlinear Anal. 63 (2005), pp. 1967–1977. | Zbl 1224.35140

[11] S. Oruganti - R. Shivaji, Existence results for classes of p -Laplacian semipositone equations, Bound. Value Probl. (2006), Art. ID 87483, 7 pp. | MR 2211402 | Zbl 1136.35386

[12] K. Perera - Z. Zhang, Nontrivial solutions of Kirchhoff-type problems via the Yang index, J. Differential Equations 221 (2006), no. 1, pp. 246–255. | MR 2193850 | Zbl 05013580

[13] B. Ricceri, On an elliptic Kirchhoff-type problem depending on two parameters, J. Global Optim. 46 (2010), no. 4, pp. 543–549. | MR 2601787 | Zbl 1192.49007

[14] J.J. Sun - C.L. Tang, Existence and multiplicity of solutions for Kirchhoff type equations, Nonlinear Anal. 74 (2011), pp. 1212–1222. | MR 2746801 | Zbl 1209.35033

[15] M.H. Yang - Z.Q. Han, Existence and multiplicity results for Kirchhoff type problems with four-superlinear potentials, Appl. Anal. 91 (2012), no. 11, pp. 2045–2055. | MR 2983999 | Zbl 1260.35060

[16] Z. Zhang - K. Perera, Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow, J. Math. Anal. Appl. 317 (2006), no. 2, pp. 456–463. | MR 2208932 | Zbl 1100.35008