Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function
Using bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign-changing or constant sign solutions for the boundary value problems u″+a(t)f(u)=0, t∈(0, 1), u(0)=0, and u(1)=0, where f∈C(ℝ,ℝ) satisfies f(0)=0 and the limits f∞=lim|s|→∞(f(s)/s), f0=lim|s|→0(...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/897307 |
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| author | Yulian An |
| author_facet | Yulian An |
| author_sort | Yulian An |
| collection | DOAJ |
| description | Using bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign-changing or constant sign solutions for the boundary value problems u″+a(t)f(u)=0, t∈(0, 1), u(0)=0, and u(1)=0, where f∈C(ℝ,ℝ) satisfies f(0)=0 and the limits f∞=lim|s|→∞(f(s)/s), f0=lim|s|→0(f(s)/s)∈{0,∞}. Weight function a(t)∈C1[0,1] satisfies a(t)>0 on [0,1]. |
| format | Article |
| id | doaj-art-ca67ecefbd0f42d2aa5e292eb35d2445 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ca67ecefbd0f42d2aa5e292eb35d24452025-08-20T03:24:03ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/897307897307Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight FunctionYulian An0Department of Mathematics, Shanghai Institute of Technology, Shanghai 201418, ChinaUsing bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign-changing or constant sign solutions for the boundary value problems u″+a(t)f(u)=0, t∈(0, 1), u(0)=0, and u(1)=0, where f∈C(ℝ,ℝ) satisfies f(0)=0 and the limits f∞=lim|s|→∞(f(s)/s), f0=lim|s|→0(f(s)/s)∈{0,∞}. Weight function a(t)∈C1[0,1] satisfies a(t)>0 on [0,1].http://dx.doi.org/10.1155/2013/897307 |
| spellingShingle | Yulian An Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function Abstract and Applied Analysis |
| title | Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function |
| title_full | Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function |
| title_fullStr | Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function |
| title_full_unstemmed | Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function |
| title_short | Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function |
| title_sort | exact multiplicity of sign changing solutions for a class of second order dirichlet boundary value problem with weight function |
| url | http://dx.doi.org/10.1155/2013/897307 |
| work_keys_str_mv | AT yulianan exactmultiplicityofsignchangingsolutionsforaclassofsecondorderdirichletboundaryvalueproblemwithweightfunction |