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On the solvability of some parabolic equations involving nonlinear boundary conditions with L1 data

Taourirte Laila, Charkaoui Abderrahim, Alaa Nour Eddine

Opuscula Mathematica

2024

Vol. 44, no. 4

587--623

We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and L1 data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder’s topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models.

Reflected BSDEs with general filtration and two completely separated barriers

Topolewski Mateusz

Probability and Mathematical Statistics

2019

Vol. 39, Fasc. 1

199--218

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right-continuity and completeness. As for barriers, we assume that there are càdlàg processes of class D that are completely separated. We prove the existence and uniqueness of solutions for an integrable final condition and an integrable monotone generator. An application to the zero-sum Dynkin game is given.

On elliptic problems with a nonlinearity depending on the gradient

Chabrowski J.

Opuscula Mathematica

2009

Vol. 29, no. 4

377-391

We investigate the solvability of the Neumann problem (1.1) involving the non-linearity depending on the gradient. We prove the existence of a solution when the right hand side ƒ of the equation belongs to Lm( Ω) with 1 ≤m <2.

Existence for some quasilinear elliptic systems with critical growth nonlinearity and L 1 data

Alaa N., Maach F., Mounir I.

Journal of Applied Analysis

2005

Vol. 11, nr 1

81-94

We prove the existence of weak solutions for some quasilinear elliptic reaction-diffusion systems with Dirichlet boundary conditions and satisfying to the two main properties: the positivity of the solutions and the balance law. The nonlinearity we consider here has critical growth with respect to the gradient and data are in L1.