Existence and multiplicity of real solutions to the Helmholtz equation with concave and convex nonlinearities

ShaoXiong Chen; Biao Liu; Ruowen Qiu; Fukun Zhao

doi:10.1515/dema-2025-0227

January 1, 2026Demonstratio MathematicaOpen Access

Existence and multiplicity of real solutions to the Helmholtz equation with concave and convex nonlinearities

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Key Points

To explore the existence and multiplicity of real solutions for the nonlinear Helmholtz equation.
Analyzed the nonlinear Helmholtz equation within the context of asymptotic conditions.
Considered cases with convex and concave nonlinearities.
Applied mathematical techniques to establish conditions for solutions.
Identified conditions under which multiple real solutions exist.
Showed the dependence of solutions on the nature of the nonlinearity.
Established asymptotic behavior of solutions as x approaches infinity.

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Implication

This research demonstrates the existence and multiplicity of real solutions to the Helmholtz equation, indicating significant findings in nonlinear dynamics.

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Cite This Study

Chen et al. (2026) studied this question.

synapsesocial.com/papers/69e07d3c2f7e8953b7cbe51a https://doi.org/10.1515/dema-2025-0227

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Existence and multiplicity of real solutions to the Helmholtz equation with concave and convex nonlinearities

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Existence and multiplicity of real solutions to the Helmholtz equation with concave and convex nonlinearities

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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