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Abstract:

Variational techniques were used to prove the existence of nontrivial solutions to the fourth order elliptic equation with nonlinear boundary conditions. Abstract results from the critical point theory, some topological tools and Sobolev trace inequalities were used to deal with the boundary terms of the subcritical superlinear nonlinearity problem. A critical nonlinearity with a sublinear perturbation was studied by applying concentration compactness method combined with topological arguments.

Registro:

Documento: Artículo
Título:A fourth order elliptic equation with nonlinear boundary conditions
Autor:Fernández Bonder, J.; Rossi, J.D.
Filiación:Departamento De Matemática, FCEyN, UBA (1428), Buenos Aires, Argentina
Palabras clave:Bilaplacian; Nonlinear boundary conditions; Variational problems; Boundary conditions; Mathematical operators; Perturbation techniques; Variational techniques; Elliptic equations; Nonlinear equations
Año:2002
Volumen:49
Número:8
Página de inicio:1037
Página de fin:1047
DOI: http://dx.doi.org/10.1016/S0362-546X(01)00718-0
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v49_n8_p1037_FernandezBonder

Referencias:

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  • Bernis, F., Garcia-Azorero, J., Peral, I., Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order (1996) Adv. Differential Equations, 1 (2), pp. 219-240
  • Chipot, M., Shafrir, I., Fila, M., On the solutions to some elliptic equations with nonlinear Neumann boundary conditions (1996) Adv. Differential Equations, 1 (1), pp. 91-110
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  • Hu, B., Non existence of a positive solution of the Laplace equation with a nonlinear boundary condition (1994) Differential Integral Equations, 7, pp. 301-313
  • Krasnoselski, M.A., (1964) Topological methods in the theory of nonlinear integral equations, , Macmillan, New York
  • Lions, P.L., The concentration-compactness principle in the calculus of variations, The limit case, part 1 (1985) Rev. Mat. Iberoamericana, 1 (1), pp. 145-201
  • Lions, P.L., The concentration-compactness principle in the calculus of variations, The limit case, part 2 (1985) Rev. Mat. Iberoamericana, 1 (2), pp. 45-121
  • Noussair, E.S., Swanson, C.A., Jianfu, Y., Critical semilinear biharmonic equations in RN (1992) Proc. Roy. Soc. Edinburgh, 121 A, pp. 139-148
  • Pucci, P., Serrin, J., Critical exponents and critical dimensions for polyharmonic operators (1990) J. Math. Pure Appl., 69, pp. 55-83
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Citas:

---------- APA ----------
Fernández Bonder, J. & Rossi, J.D. (2002) . A fourth order elliptic equation with nonlinear boundary conditions. Nonlinear Analysis, Theory, Methods and Applications, 49(8), 1037-1047.
http://dx.doi.org/10.1016/S0362-546X(01)00718-0
---------- CHICAGO ----------
Fernández Bonder, J., Rossi, J.D. "A fourth order elliptic equation with nonlinear boundary conditions" . Nonlinear Analysis, Theory, Methods and Applications 49, no. 8 (2002) : 1037-1047.
http://dx.doi.org/10.1016/S0362-546X(01)00718-0
---------- MLA ----------
Fernández Bonder, J., Rossi, J.D. "A fourth order elliptic equation with nonlinear boundary conditions" . Nonlinear Analysis, Theory, Methods and Applications, vol. 49, no. 8, 2002, pp. 1037-1047.
http://dx.doi.org/10.1016/S0362-546X(01)00718-0
---------- VANCOUVER ----------
Fernández Bonder, J., Rossi, J.D. A fourth order elliptic equation with nonlinear boundary conditions. Nonlinear Anal Theory Methods Appl. 2002;49(8):1037-1047.
http://dx.doi.org/10.1016/S0362-546X(01)00718-0