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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.

Positive solutions of boundary value problems with nonlinear nonlocal boundary conditions

Padhi S., Pati S., Hota D. K.

Opuscula Mathematica

2016

Vol. 36, no. 1

69--79

We consider the existence of at least three positive solutions of a nonlinear first order problem with a nonlinear nonlocal boundary condition given by [formula] where r : [0,1] → [0, ∞) is continuous; the nonlocal points satisfy [formula] the nonlinear function ƒi and [formula] are continuous mappings from [0,1] x [0,∞) → [0,∞) for i = 1,2,... ,m and j = 1, 2,. .. , n respectively, and λ > 0 is a positive parameter.

On the existence of nontrivial solutions for nonlocal elliptic Kirchhoff type problems with nonlinear boundary conditions

Rasouli S. H., Salehi B.

Fasciculi Mathematici

2015

Nr 55

183--188

In this paper, by using the Mountain Pass Lemma, we study the existence of nontrivial solutions for a nonlocal elliptic Kirchhoff type equation together with nonlinear boundary conditions.