TY - JOUR
T1 - Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem
AU - Graef, John R.
AU - Kong, Lingju
AU - Wang, Haiyan
N1 - Funding Information:
The research of J.R. Graef was supported in part by the Office of Academic and Research Computing Services of the University of Tennessee at Chattanooga.
PY - 2008/9/1
Y1 - 2008/9/1
N2 - The authors consider the boundary value problem{(y″ - ρ2 y + λ g (t) f (y) = 0, 0 ≤ t ≤ 2 π,; y (0) = y (2 π), y′ (0) = y′ (2 π) .) Under different combinations of superlinearity and sublinearity of the function f, various existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ. The uniqueness of solutions and the dependence of solutions on the parameter λ are also studied. The results are illustrated with an example.
AB - The authors consider the boundary value problem{(y″ - ρ2 y + λ g (t) f (y) = 0, 0 ≤ t ≤ 2 π,; y (0) = y (2 π), y′ (0) = y′ (2 π) .) Under different combinations of superlinearity and sublinearity of the function f, various existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ. The uniqueness of solutions and the dependence of solutions on the parameter λ are also studied. The results are illustrated with an example.
KW - Dependence on a parameter
KW - Existence of positive solutions
KW - Krasnosel'skii's theorem
KW - Multiplicity of positive solutions
KW - Periodic boundary value problem
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U2 - 10.1016/j.jde.2008.06.012
DO - 10.1016/j.jde.2008.06.012
M3 - Article
AN - SCOPUS:46449089630
SN - 0022-0396
VL - 245
SP - 1185
EP - 1197
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 5
ER -