On the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problems
We consider the boundary value problem −u″(x)=λf(u(x)), x∈(0,1); u′(0)=0; u′(1)+αu(1)=0, where α>0, λ>0 are parameters and f∈c2[0,∞) such that f(0)<0. In this paper, we study for the two cases ρ=0 and ρ=θ (ρ is the value of the solution at x=0 and θ is such that F(θ)=0 where F(s)=∫0sf(t)dt...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202109276 |
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| author | G. A. Afrouzi M. Khaleghy Moghaddam |
| author_facet | G. A. Afrouzi M. Khaleghy Moghaddam |
| author_sort | G. A. Afrouzi |
| collection | DOAJ |
| description | We consider the boundary value problem −u″(x)=λf(u(x)), x∈(0,1); u′(0)=0; u′(1)+αu(1)=0, where α>0, λ>0 are parameters and f∈c2[0,∞) such that f(0)<0. In this paper, we study for the two cases ρ=0 and ρ=θ (ρ is the value of the solution at x=0 and θ is such that F(θ)=0 where F(s)=∫0sf(t)dt) the relation between λ and the number of interior critical points of the nonnegative solutions of the above system. |
| format | Article |
| id | doaj-art-bac24d2a57584b70bb841d2a0eb98f38 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bac24d2a57584b70bb841d2a0eb98f382025-02-03T07:25:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01311275176010.1155/S0161171202109276On the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problemsG. A. Afrouzi0M. Khaleghy Moghaddam1Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, IranDepartment of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, IranWe consider the boundary value problem −u″(x)=λf(u(x)), x∈(0,1); u′(0)=0; u′(1)+αu(1)=0, where α>0, λ>0 are parameters and f∈c2[0,∞) such that f(0)<0. In this paper, we study for the two cases ρ=0 and ρ=θ (ρ is the value of the solution at x=0 and θ is such that F(θ)=0 where F(s)=∫0sf(t)dt) the relation between λ and the number of interior critical points of the nonnegative solutions of the above system.http://dx.doi.org/10.1155/S0161171202109276 |
| spellingShingle | G. A. Afrouzi M. Khaleghy Moghaddam On the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problems International Journal of Mathematics and Mathematical Sciences |
| title | On the relation between interior critical points of positive
solutions and parameters for a class of nonlinear boundary value problems |
| title_full | On the relation between interior critical points of positive
solutions and parameters for a class of nonlinear boundary value problems |
| title_fullStr | On the relation between interior critical points of positive
solutions and parameters for a class of nonlinear boundary value problems |
| title_full_unstemmed | On the relation between interior critical points of positive
solutions and parameters for a class of nonlinear boundary value problems |
| title_short | On the relation between interior critical points of positive
solutions and parameters for a class of nonlinear boundary value problems |
| title_sort | on the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problems |
| url | http://dx.doi.org/10.1155/S0161171202109276 |
| work_keys_str_mv | AT gaafrouzi ontherelationbetweeninteriorcriticalpointsofpositivesolutionsandparametersforaclassofnonlinearboundaryvalueproblems AT mkhaleghymoghaddam ontherelationbetweeninteriorcriticalpointsofpositivesolutionsandparametersforaclassofnonlinearboundaryvalueproblems |