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Solvability for a Nonlinear Three-Point Boundary Value Problem with P-Laplacian-Like Operator at Resonance
García-Huidobro et al. - 2001 - Solvability for a nonlinear three-point boundary v.pdf
García-Huidobro et al. - 2001 - Solvability for a nonlinear three-point boundary v.pdf (1.902Mb)
The purpose of this paper is to study the following three-point boundary
value problem which contains the nonlinear operator (φ(u
= f (t, u, u
(a) = 0, u(η) = u(b), (1.1)
where η ∈ (a, b) is given. We are interested in the case when problem (1.1) is
at resonance, meaning by this that the associated three-point boundary value
= 0 a < t < b,
(a) = 0, u(η) = u(b) (1.2)
has the nontrivial solution u(t) = A, where A ∈ R is an arbitrary constant. For
the linear operator, three-point boundary value problems at resonance have been
recently studied in [3, 11].