Abstract
In this work we provide an existence and location result for the third-order nonlinear differential equation u ‴ ( t ) = f ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) ) , where f : [ a , b ] × R 3 → R is a continuous function, and two types of boundary conditions: u ( a ) = A , ϕ ( u ′ ( b ) , u ″ ( b ) ) = 0 , u ″ ( a ) = B , or u ( a ) = A , ψ ( u ′ ( a ) , u ″ ( a ) ) = 0 , u ″ ( b ) = C , with ϕ , ψ : R 2 → R continuous functions, monotonous in the second variable and A , B , C ∈ R . We assume that f satisfies a sign-type Nagumo condition which allows an asymmetric unbounded behaviour on the nonlinearity. The arguments used concern Leray–Schauder degree theory and lower and upper solutions technique.
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