Nonlinear scalar multipoint boundary value problems at resonance. Issue 12 (2nd December 2018) - Maroncelli, Daniel
ABSTRACT: In this work we provide conditions for the existence of solutions to nonlinear boundary value problems of the formy ( t + n ) + a n − 1 ( t ) y ( t + n − 1 ) + ⋯ a 0 ( t ) y ( t ) = g ( t, y ( t + m − 1 ) ) subject to∑ j = 1 n b i j ( 0 ) y ( j − 1 ) + ∑ j = 1 n b i j ( 1 ) y ( j ) + ⋯ + ∑ j = 1 n b i j ( N ) y ( j + N − 1 ) = 0 fori = 1, …, n . The existence of solutions will be proved under a mild growth condition on the nonlinearity, g, which must hold only on a bounded subset of 0, …, N × R .