Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : On the solvability of a boundary value problem on the real line | Cupini et al. Boundary Value Problems 2011 2011 26 http content 2011 1 26 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access On the solvability of a boundary value problem on the real line Giovanni Cupini1 Cristina Marcelli2 and Francesca Papalini2 Correspondence papalini@ 2Dipartimento di Scienze Matematiche - Università Politecnica delle Marche Via Brecce Bianche 60131 Ancona Italy Full list of author information is available at the end of the article Springer Abstract We investigate the existence of heteroclinic solutions to a class of nonlinear differential equations a x O x t f t x t x t . t e R governed by a nonlinear differential operator F extending the classical p-Laplacian with right-hand side f having the critical rate of decay -1 as t that is f t t We prove general existence and non-existence results as well as some simple criteria useful for right-hand side having the product structure f t x x b t x c x x . Mathematical subject classification Primary 34B40 34C37 Secondary 34B15 34L30. Keywords boundary value problems unbounded domains heteroclinic solutions nonlinear differential operators p-Laplacian operator F o -Laplacian operator 1. Introduction Differential equations governed by nonlinear differential operators have been extensively studied in the last decade due to their several applications in various sciences. The most famous differential operator is the well-known Ji-Laplacian and its generalization to the generic F-Laplacian operator an increasing homeomorphism of R with 0 0 0 . Many articles have been devoted to the study of differential equations of the type O x t f t x t x t for F-Laplacian operators and recently also the study of singular or non-surjective differential operators has become object of an increasing interest see . 1-10 . On the other hand in many applications the dynamic is described by a differential operator also depending on the state variable like a x
