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September 5, 2025

Multiple solutions to relativistic systems with potential boundary conditions

Key Points

The analysis reveals multiple solutions to relativistic systems under specific boundary conditions, emphasizing their importance in mathematical physics.
Utilizing a variational approach, the study identifies solutions when the action functional is even, demonstrating robustness in this methodology.
Distinct geometrical solutions were found, linked to invariance in action functionals, suggesting wider implications for the theory of differential equations.
The results stress the necessity of considering the convex nature of the function within boundary constraints, opening pathways for future research.

Abstract

Abstract We consider potential systems of differential equations of the form equation* - (u^) ^ = ᵤ F (t, u), in 0, T, equation* under the general boundary condition equation* ( (u^) (0), - (u^) (T) ) j (u (0), u (T) ), equation* where (y) =y/1- |y|² and j: RN RN (-, +] is convex and lower semicontinuous. Making use of the variational approach introduced in the recent paper “Potential systems with singular -Laplacian”, we obtain multiplicity of solutions when the action functional is even, as well as existence of multiple geometrically distinct solutions when this functional is invariant with respect to some discrete group.

Multiple solutions to relativistic systems with potential boundary conditions

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Abstract

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