Existence of positive solutions for a class of BVPs in Banach spaces
DOI:
https://doi.org/10.24193/subbmath.2021.4.10Keywords:
Boundary value problem, Green’s function, unbounded interval, mea- sure of noncompactness, fixed point index, sum operator.Abstract
In this work, we use index fixed point theory for perturbation of expansive mappings by £-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear differential equation on the positive half-line. The nonlinearity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave differently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main results is given.
Mathematics Subject Classification (2010): 34B15, 34B18, 34B40, 47H08, 47H10.
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