Displaying similar documents to “Existence of nonzero nonnegative solutions of semilinear equations at resonance”

Problems with nonlinear boundary value conditions

Michal Fečkan (1992)

Commentationes Mathematicae Universitatis Carolinae

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The existence and multiplicity results are shown for certain types of problems with nonlinear boundary value conditions.

Solvability of a higher-order multi-point boundary value problem at resonance

Xiaojie Lin, Qin Zhang, Zengji Du (2011)

Applications of Mathematics

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Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance x ( n ) ( t ) = f ( t , x ( t ) , x ' ( t ) , ⋯ , x ( n - 1 ) ( t ) ) , t ∈ ( 0 , 1 ) , x ( 0 ) = ∑ i = 1 m α i x ( ξ i ) , x ' ( 0 ) = ⋯ = x ( n - 2 ) ( 0 ) = 0 , x ( n - 1 ) ( 1 ) = ∑ j = 1 l β j x ( n - 1 ) ( η j ) , where f : [ 0 , 1 ] × ℝ n → ℝ is a Carathéodory function, 0 < ξ 1 < ξ 2 < ⋯ < ξ m < 1 , α i ∈ ℝ , i = 1 , 2 , ⋯ , m , m ≥ 2 and 0 < η 1 < ⋯ < η l < 1 , β j ∈ ℝ , j = 1 , ⋯ , l , l ≥ 1 . In this paper, two of the boundary value conditions are responsible for resonance.