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- Cheng, Yuanji
(författare)
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Boundary blow-up insemilinear elliptic problems with singular weights at the boundary
- 2001
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Ingår i: Applicable Mathematics. - : Narosa publishing house, New Delhi. - 8173194068 ; , s. 68-81
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we study under what conditions on m(x) and f(u) the problem Δu=m(x)f(u) has a solution in a bounded domain D, which tends to infinity, as x tends to the boundary. We show that if m(x) is singular at the boundary of D, except that the Keller-Osserman condition must hold, the growth of f at the infinity has to be slow for a solution to exist. Some existence results have been established.
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| 2. |
- Cheng, Yuanji
(författare)
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Multiple solutions for prescribed boundary value problem
- 2002
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Ingår i: Nonlinear Analysis. - : Elsevier Science Ltd.. - 0362-546X .- 1873-5215. ; 51:3, s. 537-552
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Tidskriftsartikel (refereegranskat)abstract
- We, in this paper, consider the semilinear elliptic boundary value problem - ∆u = f(x, u) in Ω and u = g on ∂Ω and the corresponding Bolza problem x'' + ∂V(t, x) =0, x(0)= x0, x(T)= x1, where Ω is a bounded open subset in R^n with C² boundary and g is a given continuous function on the boundary of Ω; and T is the given traveling time, x0,x1 are two fixed points in the state space Rn. Under certain conditions on f and V, we show that the above problems have infinitely many solutions
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| 3. |
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| 4. |
- Cheng, Yuanji, et al.
(författare)
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Remarks on bifurcation in elliptic boundary value problems
- 2003
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Ingår i: International Conference on Differential Equations. - : World Scientific. ; , s. 1051-1055
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Konferensbidrag (refereegranskat)abstract
- In this paper, we present some observations of biurcation in nonlinear elliptic boundary value problem - ∆u = f(λ, u) in domain Ω, and u = 0 on the boundary ∂Ω. We are interested in how solution(s) depends on the parameter λ. Through examples, we show that multiple solutions appear, when λ cross certain critical value, i.e. bifurcation occurs.
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