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

Existence of weak solutions for mixed problems of parabolic systems.

Duong, Pham Trieu, Van Loi, Do (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of weak solutions for nonlinear elliptic systems on $ℝ^{N}$ .

El-Zahrani, Eada A., Serag, Hassan M. (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of weak solutions for nonlinear systems involving several $p$ -Laplacian operators.

Khafagy, Salah A., Serag, Hassan M. (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of weak solutions for quasilinear elliptic equations involving the $p$ -Laplacian.

Severo, Uberlandio (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions

Cholmin Sin, Sin-Il Ri (2022)

Mathematica Bohemica

We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided $p (x) > 2 n / (n + 2)$ . To prove this, we show Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.

Existence of weak solutions for the thermistor problem with degeneracy.

El Hachimi, Abderrahmane, Ammi, Moulay Rachid Sidi (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of weak solutions to a class of degenerate semiconductor equations modeling avalanche generation.

Wu, Bin (2009)

Mathematical Problems in Engineering

Existence of weak solutions to doubly degenerate diffusion equations

Aleš Matas, Jochen Merker (2012)

Applications of Mathematics

We prove existence of weak solutions to doubly degenerate diffusion equations $\dot{u} = Δ_{p} u^{m - 1} + f (m, p \geq 2)$ by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains $Ω \subset ℝ^{n}$ with Dirichlet or Neumann boundary conditions. The function $f$ can be an inhomogeneity or a nonlinearity involving terms of the form $f (u)$ or $div (F (u))$ . In the appendix, an introduction to weak differentiability...

Existence of weak-renormalized solution for a nonlinear system.

Blanca Climent (2002)

Revista Matemática Complutense

We prove an existence result for a coupled system of the reaction-diffusion kind. The fact that no growth condition is assumed on some nonlinear terms motivates the search of a weak-renormalized solution.

Existence result for a class of doubly nonlinear parabolic systems

Ahmed Aberqi, Jaouad Bennouna, Hicham Redwane (2014)

Applicationes Mathematicae

We prove the existence of a renormalized solution to a class of doubly nonlinear parabolic systems.

Existence result for a class of elliptic systems with indefinite weights in $ℝ^{2}$ .

Zhang, Guoqing, Liu, Sanyang (2008)

Boundary Value Problems [electronic only]

Existence result for a class of nonlinear elliptic systems on punctured unbounded domains.

Colin, Fabrice (2010)

Boundary Value Problems [electronic only]

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