Existence and multiplicity of positive solutions for a singular Riemann-Liouville fractional differential problem
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TUDORACHE, Rodica Luca. Existence and multiplicity of positive solutions for a singular Riemann-Liouville fractional differential problem. In: Mathematics and IT: Research and Education. 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, pp. 53-54.
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Mathematics and IT: Research and Education 2021
Conferința "Mathematics and IT: Research and Education "
Chişinău, Moldova, 1-3 iulie 2021

Existence and multiplicity of positive solutions for a singular Riemann-Liouville fractional differential problem


Pag. 53-54

Tudorache Rodica Luca
 
Gheorghe Asachi Technical University of Iasi
 
Disponibil în IBN: 30 iunie 2021


Rezumat

We study the nonlinear fractional differential equationformulawith the integral-differential boundary conditionsformulawhere  formula for all formula  denotes the Riemann-Liouville derivative of order k (for k = ®; ¯0; ¯1; : : : ; ¯m), the integrals from the boundary conditions (2) are Riemann-Stieltjes integrals with Hi, i = 1; : : : ;m, functions of bounded variation, the functions   formula   and the nonlinearity f is nonnegative and it may be singular at the points t = 0, t = 1 and/or x = 0. We will present conditions for the data of problem (1),(2) connected to the spectral radii of some associated linear operators such that this problem has at least one or two positive solutions (x(t) > 0 for all t 2 (0; 1]). In the proof of the main existence theorems we use an application of the KreinRutman theorem in the space C[0; 1] and the fixed point index theory (see [1]).