Second-order boundary value problems with nonhomogeneous boundary conditions (II) |
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| Authors: | Lingju Kong Qingkai Kong |
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| Affiliation: | aDepartment of Mathematics, The University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA;bDepartment of Mathematics, Northern Illinois University, Dekalb, IL 60115, USA |
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| Abstract: | Sufficient conditions are given for the existence of solutions of the following nonlinear boundary value problem with nonhomogeneous multi-point boundary condition We prove that the whole plane  is divided by a “continuous decreasing curve” Γ into two disjoint connected regions ΛE and ΛN such that the above problem has at least one solution for (λ1,λ2) Γ, has at least two solutions for (λ1,λ2)ΛE Γ, and has no solution for (λ1,λ2)ΛN. We also find explicit subregions of ΛE where the above problem has at least two solutions and two positive solutions, respectively. |
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| Keywords: | Nonhomogeneous multi-point BVPs Existence of solutions Lower and upper solutions Leray– Schauder degree |
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