Exact Solution and Bifurcation Curve for the Minkowski-Curvature Equation with Nonlinearity u p + u q, p > 1

Yan-Hsiou Cheng and Kuo-Chih Hung ()
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Yan-Hsiou Cheng: Department of Mathematics and Information Education, National Taipei University of Education, Taipei City 106, Taiwan
Kuo-Chih Hung: Fundamental General Education Center, National Chin-Yi University of Technology, Taichung 411, Taiwan

Mathematics, 2025, vol. 13, issue 22, 1-10

Abstract: We study the bifurcation curve and exact multiplicity of positive solutions in the space C 2 ( − L , L ) ∩ C [ − L , L ] for the Minkowski-curvature equation: − u ′ ( x ) 1 − u ′ ( x ) 2 ′ = λ u p + u q , − L < x < L ; u ( − L ) = u ( L ) = 0 , where λ , L > 0 and p > 1 . If 1 < p < q ≤ 2 p + 3 p 2 − 3 , we prove that the bifurcation curve is ⊂-shaped.

Keywords: positive solution; exact multiplicity; bifurcation curve; Minkowski-curvature equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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