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AFROUZI, G. A., JAFARI, M.. (1384). EXISTENCE RESULTS FOR A CLASS OF SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS. , 29(2), 296-304. doi: 10.22099/ijsts.2005.2805
G. A. AFROUZI; M. JAFARI. "EXISTENCE RESULTS FOR A CLASS OF SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS". , 29, 2, 1384, 296-304. doi: 10.22099/ijsts.2005.2805
AFROUZI, G. A., JAFARI, M.. (1384). 'EXISTENCE RESULTS FOR A CLASS OF SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS', , 29(2), pp. 296-304. doi: 10.22099/ijsts.2005.2805
AFROUZI, G. A., JAFARI, M.. EXISTENCE RESULTS FOR A CLASS OF SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS. , 1384; 29(2): 296-304. doi: 10.22099/ijsts.2005.2805

EXISTENCE RESULTS FOR A CLASS OF SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

Iranian Journal of Science
مقاله 7، دوره 29، شماره 2، آذر 2005، صفحه 296-304    اصل مقاله (212.67 K)
نوع مقاله: Regular Paper
شناسه دیجیتال (DOI): 10.22099/ijsts.2005.2805
نویسندگان
G. A. AFROUZI* ؛ M. JAFARI
Department of Mathematics, Faculty of Basic Sciences Mazandaran University, Babolsar, I. R. of Iran
چکیده
We consider the semilinear elliptic boundary value problem
  
= ∈∂Ω
− Δ = ∈Ω
u x x
u x f u x x
( ) 0;
( ) λ ( ( ));
where λ > 0 is a parameter, Ω is a bounded region in RN with a smooth boundary, and f is a
smooth function. We prove, under some additional conditions, the existence of a positive solution for λ
large. We prove that our solution u for λ large is such that = →∞
∈Ω
|| u ||: sup| u(x) |
x
as λ →∞.
Also, in the case of N = 1, we use a bifurcation theory to show that the solution is unstable.
کلیدواژه‌ها
Semilinear elliptic problem؛ positive solution؛ unstable solution
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