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- W373548660 abstract "We are interested in the existence of nontrivial solutions for the second order nonlinear differential equation (E): y′′(t) = f ( t, y(t) ) = 0, 0 < t < 1 subject to multipoint boundary conditions at t = 1 and either Dirichlet or Neumann conditions at t = 0. Assume that f(t, y) satisfies |f(t, y)| ≤ k(t)|y| + h(t) for non-negative functions k, h ∈ L(0, 1) for all (t, y) ∈ (0, 1) × R and f(t, 0) 6≡ 0 for t ∈ (0, 1). We show without any additional assumption on h(t) that if ‖k‖1 is sufficiently small where ‖ · ‖1 denotes the norm of L(0, 1) then there exists at least one non-trivial solution for such boundary value problems. Our results reduce to that of Sun and Liu [11] and Sun [10] for the three point problem with Neumann boundary condition at t = 0." @default.
- W373548660 created "2016-06-24" @default.
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- W373548660 date "2010-01-01" @default.
- W373548660 modified "2023-09-26" @default.
- W373548660 title "Existence theorems for second order multi-point boundary value problems" @default.
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- W373548660 doi "https://doi.org/10.14232/ejqtde.2010.1.41" @default.
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