Search results for "Mixed conditions"

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EXISTENCE OF THREE SOLUTIONS FOR A MIXED BOUNDARY VALUE PROBLEM WITH THE STURM-LIOUVILLE EQUATION

2012

Abstract. The aim of this paper is to establish the existence of threesolutions for a Sturm-Liouville mixed boundary value problem. The ap-proach is based on multiple critical points theorems. 1. IntroductionThe aim of this paper is to establish, under a suitable set of assumptions, theexistence of at least three solutions for the following Sturm-Liouville problemwith mixed boundary conditions(RS λ )ˆ−(pu ′ ) ′ +qu = λf(t,u) in I =]a,b[u(a) = u ′ (b) = 0,where λ is a positive parameter and p, q, f are regular functions. To be precise,if f : [a,b] × R→ Ris a L 2 -Carath´eodory function and p,q ∈ L ∞ ([a,b]) suchthatp 0 := essinf t∈[a,b] p(t) > 0, q 0 := essinf t∈[a,b] q(t) ≥ 0,then we prove …

CombinatoricsSettore MAT/05 - Analisi MatematicaGeneral MathematicsMathematical analysisBoundary value problem mixed conditionsInterval (graph theory)Sturm–Liouville theoryFunction (mathematics)Boundary value problemMathematicsBulletin of the Korean Mathematical Society
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Two non-zero solutions for Sturm–Liouville equations with mixed boundary conditions

2019

Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem.

Sturm–Liouville theoryCritical points01 natural sciencesCritical point (mathematics)Critical pointSturm–Liouville equationVariational methodsBoundary value problem0101 mathematicsBoundary value problem; Critical points; Mixed conditions; Sturm–Liouville equation; Variational methodsBoundary value problemMathematicsApplied Mathematics010102 general mathematicsMathematical analysisGeneral EngineeringVariational methodAnalysiGeneral MedicineMathematics::Spectral Theory010101 applied mathematicsComputational MathematicsMixed conditionGeneral Economics Econometrics and FinanceMixed conditionsAnalysis
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