Geodesic
Generalized boundary value problems with linear growth
Mathematica Bohemica, Tome 123 (1998) no. 4, pp. 385-404

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It is shown that for a given system of linearly independent linear continuous functionals $l_i C^{n-1} \to\bb R$, $i=1,\dots,n$, the set of all $n$-th order linear differential equations such that the Green function for the corresponding generalized boundary value problem (BVP for short) exists is open and dense in the space of all $n$-th order linear differential equations. Then the generic properties of the set of all solutions to nonlinear BVP-s are investigated in the case when the nonlinearity in the differential equation has a linear majorant. A periodic BVP is also studied.
It is shown that for a given system of linearly independent linear continuous functionals $l_i C^{n-1} \to\bb R$, $i=1,\dots,n$, the set of all $n$-th order linear differential equations such that the Green function for the corresponding generalized boundary value problem (BVP for short) exists is open and dense in the space of all $n$-th order linear differential equations. Then the generic properties of the set of all solutions to nonlinear BVP-s are investigated in the case when the nonlinearity in the differential equation has a linear majorant. A periodic BVP is also studied.
DOI : 10.21136/MB.1998.125969
Classification : 34B15, 34B27, 34C11, 34C25
Keywords: generic properties; periodic boundary value problem 
Šeda, Valter. Generalized boundary value problems with linear growth. Mathematica Bohemica, Tome 123 (1998) no. 4, pp. 385-404. doi: 10.21136/MB.1998.125969
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