scholarly journals Existence of solutions and positivity of the infimum eigenvalue for degenerate elliptic equations with variable exponents

2013 ◽  
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Variable Exponents ◽  
Degenerate Elliptic

scholarly journals Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

2019 ◽  
Vol 5 (2) ◽  
pp. 164-178
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.in the setting of the weighted Sobolev spaces.

scholarly journals Existence of a weak bounded solution for nonlinear degenerate elliptic equations in Musielak-Orlicz spaces

2020 ◽  
Vol 6 (1) ◽  
pp. 16-33 ◽  
Author(s):  
M. Bourahma ◽  
J. Bennouna ◽  
M. El Moumni
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Bounded Solution ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper, we show the existence of solutions for the nonlinear elliptic equations of the form\left\{ {\matrix{ { - {\rm{div}}\,a\left( {x,u,\nabla u} \right) = f,} \hfill \cr {u \in W_0^1L\varphi \left( \Omega \right) \cap {L^\infty }\left( \Omega \right),} \hfill \cr } } \right.where a\left( {x,s,\xi } \right) \cdot \xi \ge \bar \varphi _x^{ - 1}\left( {\varphi \left( {x,h\left( {\left| s \right|} \right)} \right)} \right)\varphi \left( {x,\left| \xi \right|} \right) and h : ℝ+→]0, 1] is a continuous decreasing function with unbounded primitive. The second term f belongs to LN(Ω) or to Lm(Ω), with m = {{rN} \over {r + 1}} for some r > 0 and φ is a Musielak function satisfying the Δ2-condition.

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