A nonexistence result for a nonlinear PDE with Robin condition
Under the assumption λ>0 and f verifying f(x,y,0)=0 in D, 2F(x,y,u)−uf(x,y,u)≥0, u≠0, and if Ω=R×D, we show the convexity of function E(t)=∬D|u(t,x,y)|2dxdy, where u:Ω→ℝ is a solution of problem λ(∂2u/∂t2)−(∂/∂x)(p(x,y)(∂u/∂x))−(∂/∂y)(q(x,y)(∂u/∂y))+f(x,y,u)=0 in Ω, u+ε(∂u/∂n)=0 on ∂Ω, considered...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/62601 |
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