AN ABSTRACT ELLIPTIC KIRCHHOFF-TYPE PROBLEM

II INTERACTIVE MEETING OF APPLIED MATHEMATICS
II EIM@ 2009
AN ABSTRACT ELLIPTIC KIRCHHOFF-TYPE PROBLEM
EUGENIO CABANILLAS LAPA1 AND VICTOR E. CARRERA BARRANTES2
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Abstract.
In a real Hilbert space H, we study solvability of the abstract elliptic problem
M (|A1/2 u|2 )Au = F (u, A1/2 u)
(1)
where A is a positive densely defined selfadjoint linear operator in H, F is a nonlinear
operator mapping H into itself and M : R → R is a C1 –class function.
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1 Instituto
de Investigación de Matemática.
Mayor de San Marcos. Lima-Perú.
E-mail address: [email protected]
Facultad de Ciencias Matemáticas.
Universidad Nacional
2 Instituto de Investigación de Matemática.
Mayor de San Marcos. Lima-Perú.
E-mail address: [email protected]
Facultad de Ciencias Matemáticas.
Universidad Nacional