Existence of positive solutions for some kinds of BVPs in Banach spaces

Lyna Benzenati, Svetlin Georgiev Georgiev, Karima Mebarki


In this work, we use index fixed point theory for perturbation of expansive mappings by $\ell$-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 posed 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 their derivative, take values in a general Banach space and have at most polynomial growth conditions. An example to illustrate the main results is given.


Boundary value problem; Green's function; unbounded interval; measure of noncompactness; fixed point index; sum operator.

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DOI: http://dx.doi.org/10.24193/subbmath.2021.4.10


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