scholarly journals NUMERICAL METHODS FOR COUPLED SYSTEMS OF QUASILINEAR ELLIPTIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

2016 ◽  
Vol 6 (2) ◽  
pp. 543-581
Author(s):  
C. V. Pao ◽  
◽  
Taiping He ◽  
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Elliptic Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Coupled Systems ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic

Multiple solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions

2010 ◽  
Vol 140 (2) ◽  
pp. 259-272 ◽  
Author(s):  
Nguyen Thanh Chung ◽  
Quôc-Anh Ngô
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Nonlinear Boundary ◽  
Smooth Boundary ◽  
Nonlinear Boundary Conditions ◽  
Quasilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Image Position ◽  
Quasilinear Elliptic ◽  
Outer Unit

Using variational methods we study the non-existence and multiplicity of non-negative solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions of the formwhere Ω; is a bounded domain with smooth boundary, n is the outer unit normal to ∂Ω and λ is a parameter. Furthermore, we want to emphasize that g : ∂Ω × [0,∞)→ ℝ is a continuous function that may or may not satisfy the Ambrosetti–Rabinowitz-type condition.

Positive solutions of elliptic equations with nonlinear boundary conditions

2009 ◽  
Vol 70 (1) ◽  
pp. 328-334 ◽  
Author(s):  
Xiuchao Song ◽  
Weihua Wang ◽  
Peihao Zhao
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions
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