Existence of Positive Solutions of a Semilinear Elliptic Equation in Rn + with a Nonlinear Boundary Condition
✍ Scribed by M Chipot; M Chlebı́k; M Fila; I Shafrir
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 380 KB
- Volume
- 223
- Category
- Article
- ISSN
- 0022-247X
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## Abstract The existence of travelling wave solutions for the heat equation ∂~__t__~ __u__ –Δ__u__ = 0 in an infinite cylinder subject to the nonlinear Neumann boundary condition (∂__u__ /∂__n__) = __f__ (__u__) is investigated. We show existence of nontrivial solutions for a large class of nonlin
We study the boundedness and a priori bounds of global solutions of the problem u"0 in ;(0, ¹ ), j S j R # j S j "h(u) on j ;(0, ¹ ), where is a bounded domain in 1,, is the outer normal on j and h is a superlinear function. As an application of our results we show the existence of sign-changing sta