Nontrivial solutions on a kind of fourth-order Neumann boundary value problems

Abstract Nontrivial solutions for the fourth-order Neumann boundary value problem u (4) ( t ) − 2 u ″( t ) +  u ( t ) =  f ( t , u ( t )) for all t  ∈ (0, 1) and subject to u ′(0) =  u ′(1) =  u ‴(0) =  u ‴(1) = 0 are obtained via Morse theory. To compute the critical groups at infinity of the relevant functional, we propose an approach by combining the homotopy and reduction methods.

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