Construction of solutions of integral equations with Stieltjes functionals and bifurcation parameters
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517.968 (17)
Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (245)
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DREGLEA, Aliona, SIDOROV, Nikolay, SIDOROV, Denis. Construction of solutions of integral equations with Stieltjes functionals and bifurcation parameters. In: Acta et commentationes (Ştiinţe Exacte și ale Naturii), 2021, nr. 2(12), pp. 43-49. ISSN 2537-6284. DOI: https://doi.org/10.36120/2587-3644.v12i2.43-49
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Acta et commentationes (Ştiinţe Exacte și ale Naturii)
Numărul 2(12) / 2021 / ISSN 2537-6284 /ISSNe 2587-3644

Construction of solutions of integral equations with Stieltjes functionals and bifurcation parameters

Construirea solutiilor ecuatiilor integrale cu functionale Stieltjes si parametri de bifurcatie

DOI:https://doi.org/10.36120/2587-3644.v12i2.43-49
CZU: 517.968
MSC 2010: 45D05, 37G10.

Pag. 43-49

Dreglea Aliona, Sidorov Nikolay, Sidorov Denis
 
Irkutsk National Research Technical University
 
 
Disponibil în IBN: 10 februarie 2022


Rezumat

The nonlinearVolterra integral equations with loads on the desired solution are studied. Loads are given using the Stieltjes integrals. The equations contain a parameter, for any value of which the equation has a trivial solution. The necessary and sufficient conditions on the values of the parameter are derived in the neighborhood where the equation has nontrivial real solutions.

În lucrare sunt studiate ecuat,iile integrale neliniare Volterra cu sarcini pe solut,ia dorita. Sarcinile sunt date folosind integralele Stieltjes. Ecuat,iile cont,in un parametru, pentru oricare valoare a caruia ecuat,ia are o solut,ie banala. Condit,iile necesare s, i suficiente asupra valorilor parametrului sunt obtinute în vecinatatea în care ecuatia are solutii reale nebanale.

Cuvinte-cheie
nonlinear Volterra equations, Newton–Puiseux decompositions, bifurcation points, asymptotics, Stieltjes integral, loads,

ecuatii Volterra neliniare, decompozitia Newton–Puiseux, puncte de bifurcatie, asimptotic, integrala Stieltjes, sarcini