0000000000519579

AUTHOR

Maria Dobkevich

showing 2 related works from this author

Types and Multiplicity of Solutions to Sturm–Liouville Boundary Value Problem

2015

We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.

Mathematical analysisMultiplicity (mathematics)Sturm–Liouville theoryMixed boundary conditionMathematics::Spectral Theorymultiplicity of solutionsModeling and SimulationQA1-939Nonlinear boundary value problemBoundary value problemnonlinear boundary value problemSturm–Liouville problemMathematicsAnalysisMathematicsMathematical Modelling and Analysis
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On Different Type Solutions of Boundary Value Problems

2016

We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].

Discrete mathematicsmultiple solutionsexistence010103 numerical & computational mathematicsType (model theory)01 natural sciences010101 applied mathematicsSet (abstract data type)Modeling and Simulationboundary value problemQA1-939Interval (graph theory)Boundary value problem0101 mathematicsAnalysisMathematicsMathematicsMathematical Modelling and Analysis
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