TY - JOUR
T1 - Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter
AU - Kandemir, Mustafa
AU - Mukhtarov, Oktay
AU - Yakubov, Yakov
PY - 2009/10
Y1 - 2009/10
N2 - In this study, a Birkhoff-irregular boundary value problem for linear ordinary differential equations of the second order with discontinuous coefficients and the spectral parameter has been considered. Therefore, at the discontinuous point, two additional boundary conditions (called transmission conditions) have been added to the boundary conditions. The eigenvalue parameter is of the second degree in the differential equation and of the first degree in a boundary condition. The equation contains an abstract linear operator which is (usually) unbounded in the space Lq(-1, 1). Isomorphism and coerciveness with defects 1 and 2 are proved for this problem. The case of the biharmonic equation is also studied.
AB - In this study, a Birkhoff-irregular boundary value problem for linear ordinary differential equations of the second order with discontinuous coefficients and the spectral parameter has been considered. Therefore, at the discontinuous point, two additional boundary conditions (called transmission conditions) have been added to the boundary conditions. The eigenvalue parameter is of the second degree in the differential equation and of the first degree in a boundary condition. The equation contains an abstract linear operator which is (usually) unbounded in the space Lq(-1, 1). Isomorphism and coerciveness with defects 1 and 2 are proved for this problem. The case of the biharmonic equation is also studied.
KW - Boundary value problem
KW - Coerciveness
KW - Discontinuous coefficient
KW - Eigenvalue parameter
KW - Isomorphism
KW - Problem with a defect
KW - Transmission conditions
UR - http://www.scopus.com/inward/record.url?scp=70350430898&partnerID=8YFLogxK
U2 - 10.1007/s00009-009-0011-x
DO - 10.1007/s00009-009-0011-x
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AN - SCOPUS:70350430898
SN - 1660-5446
VL - 6
SP - 317
EP - 338
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 3
ER -