Boundary Value Problems · 2009 · 216 citations · 10 references
Natural SciencesMathematicsComputational PhysicsDifferential EquationsFinite Element AnalysisBoundary ConditionsBoundary-value ProblemsExistence TheoryPartial Differential EquationsBoundary ProblemCritical PointsLipschitz ConditionsLipschitz ContinuityNondegenerate Critical PointsNonlinear Boundary-value ProblemsSturm - Liouville TheorySturm-liouville Theory
The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.
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