Nonlinear scalar multipoint boundary value problems at resonance. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Maroncelli, Daniel
• Is Part Of: Journal of difference equations and applications. Volume 24:Issue 12(2018)
• Page Start: 1935
• Page End: 1952
• Publication Date: 2018-12-02
• Subjects: Multipoint boundary value problems -- resonance -- Lyapunov-Schmidt procedure -- Brouwer's degree; 34B15; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2018.1551378
• Languages: English
• ISSNs: 1023-6198

Abstract

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 .