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On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order

Unhale S. I., Kendre Subhash D.

Journal of Applied Analysis

2020

Vol. 26, nr 2

263--272

The objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.

Existence results and a priori estimates for solutions of quasilinear problems with gradient terms

Filippucci Roberta, Lini Chiara

Opuscula Mathematica

2019

Vol. 39, no. 2

195--205

In this paper we establish a priori estimates and then an existence theorem of positive solutions for a Dirichlet problem on a bounded smooth domain in [formula] with a nonlinearity involving gradient terms. The existence result is proved with no use of a Liouviiie theorem for the limit problem obtained via the usual blow up method, in particular we refer to the modified version by Ruiz. In particular our existence theorem extends a result by Lorca and Ubilla in two directions, namely by considering a nonlinearity which includes in the gradient term a power of u and by removing the growth condition for the nonlinearity ∫ at u = 0.