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Existence of solutions for Navier problems with degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2015)

Communications in Mathematics

In this paper we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations Δ ( v ( x ) | Δ u | q - 2 Δ u ) - j = 1 n D j ω ( x ) 𝒜 j ( x , u , u ) = f 0 ( x ) - j = 1 n D j f j ( x ) , in Ω in the setting of the weighted Sobolev spaces.

Existence of solutions to the Poisson equation in L p -weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of L p , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.

Existence of solutions to the Poisson equation in L₂-weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.

Existence of weak solutions for elliptic Dirichlet problems with variable exponent

Sungchol Kim, Dukman Ri (2023)

Mathematica Bohemica

This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type - div a ( x , u , u ) + b ( x , u , u ) = 0 in Ω , u = 0 on Ω , where Ω is a bounded domain of n , n 2 . In particular, we do not require strict monotonicity of the principal part a ( x , z , · ) , while the approach is based on the variational method and results of the variable exponent function spaces.

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