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SM ISO690:2012 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 | |||||
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Pag. 53-54 | |||||
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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]). |
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