On an elliptic equation of Kirchhoff-type with a potential asymptotically linear at infinity

Mathematical and Computer Modelling

Volumn 49, Issue 5-6, 2009, Pages 1089-1096

  Bensedik, Ahmed ^a   Bouchekif, Mohammed ^a  

^a UNIVERSITY OF TLEMCEN   (Algeria)

Author keywords

Asymptotically linear at infinity; Kirchhoff's equation; Nonlocal problem; Variational methods

Indexed keywords

DIFFERENTIAL EQUATIONS;

ASYMPTOTICALLY LINEAR AT INFINITY; BOUNDARY VALUES; ELLIPTIC EQUATIONS; KIRCHHOFF; KIRCHHOFF'S EQUATION; NONLOCAL PROBLEM; POSITIVE POTENTIALS; POSITIVE SOLUTIONS; VARIATIONAL METHODS;

ASYMPTOTIC ANALYSIS;

EID: 59149092463     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2008.07.032     Document Type: Article

References (11)

1. Alves C.O., and Corrêa F.J.S.A. On the existence of solutions for a class of problem involving a nonlinear operator. Comm. Appl. Nonlinear Anal. 8 (2001) 43-56
2. Alves C.O., Corrêa F.J.S.A., and Ma T.F. Positive solutions for a quasilinear elliptic equation of Kirchhoff type. Comput. Math. Appl. 49 (2005) 85-93
3. Cerami G. Un criterio di esistenza per i punti su varietà illimitate. Rend. Acad. Sci. Let. Ist. Lombardo 112 (1978) 332-336
4. Chipot M., and Lovat B. Some remarks on nonlocal elliptic and parabolic problems. Nonlinear Anal. 30 (1997) 4619-4627
5. Chipot M., and Rodrigues J.F. On a class of nonlocal nonlinear elliptic problems. RAIRO Modél. Math. Anal. Numér. 26 (1992) 447-467
6. Corrêa F.J.S.A., Menezes S.D.B., and Ferreira J. On a class of problems involving a nonlocal operator. Appl. Math. Comput. 147 (2004) 475-489
7. de Figueiredo D.G. Positive solutions of semilinear elliptic problems. Lecture in Math. vol. 957 (1982), Springer-Verlag, Berlin 34-87
8. G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883
9. Lions J.L. On some questions in boundary value problems of mathematical physics. Contemporary Developments in Continuum Mechanics and Partial Differential Equations. North-Holland Math. Stud. vol. 30 (1978), North-Holland, Amsterdam 284-346
10. Ma T.F. Remarks on an elliptic equation of Kirchhoff type. Nonlinear Anal. 63 (2005) 1967-1977
11. Zhou H.S. An application of a Mountain Pass theorem. Acta Math. Sin. Engl. Ser. 18 (2002) 27-36