scholarly journals A concave-convex quasilinear elliptic problem subject to a nonlinear boundary condition

2011 ◽  
pp. 469-486 ◽  
Author(s):  
José C. Sabina de Lis
Keyword(s):  
Boundary Condition ◽  
Elliptic Problem ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

scholarly journals Approximation of a quasilinear elliptic equation with nonlinear boundary condition

1994 ◽  
Vol 50 (3) ◽  
pp. 405-424 ◽  
Author(s):  
T.R. Cranny
Keyword(s):  
Boundary Condition ◽  
Original Problem ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Elliptic Partial Differential Equation ◽  
Approximate Solutions ◽  
Subsequent Paper ◽  
Quasilinear Elliptic

We consider a quasilinear elliptic partial differential equation with nonlinear boundary condition under assumptions which do not allow the application of standard degree theory results or techniques such as the method of continuity. An approximation using mollifiers is introduced, allowing the application of Leray-Schauder degree theory, and homotopy arguments are then used to prove the existence of solutions to the approximating problems. A subsequent paper will discuss the question of the convergence of these approximate solutions to a classical solution of the original problem.

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