TY - JOUR
T1 - General existence principles for nonlocal boundary value problems with ø-laplacian and their applications
AU - Agarwal, Ravi P.
AU - O'Regan, Donal
AU - Staněk, Svatoslav
PY - 2006
Y1 - 2006
N2 - The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (ø(x′)) ′ = f1(t,x,x′) + f2(t,x,x′)F 1X + f3(t,x,x′)f2x,α(x) = 0, β(x) = 0, where fj satisfy local Carathéodory conditions on some [0,T] × Dj ⊂ ℝ, fj are either regular or have singularities in their phase variables (j = 1,2,3), f i, : C1[0.T] → C0[0,T] (i = 1,2), and α,β : C1[0.T] → ℝ are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles to singular BVPs are given.
AB - The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (ø(x′)) ′ = f1(t,x,x′) + f2(t,x,x′)F 1X + f3(t,x,x′)f2x,α(x) = 0, β(x) = 0, where fj satisfy local Carathéodory conditions on some [0,T] × Dj ⊂ ℝ, fj are either regular or have singularities in their phase variables (j = 1,2,3), f i, : C1[0.T] → C0[0,T] (i = 1,2), and α,β : C1[0.T] → ℝ are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles to singular BVPs are given.
UR - https://www.scopus.com/pages/publications/33645156971
U2 - 10.1155/AAA/2006/96826
DO - 10.1155/AAA/2006/96826
M3 - Article
SN - 1085-3375
VL - 2006
SP - 1
EP - 30
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
ER -