What question did this study set out to answer?

This research aims to investigate the existence of solutions for a class of coupled logistic equations with specific boundary conditions.

April 27, 2026Advances in Calculus of Variations0 citationsOpen Access

The Nehari manifold method for a class of logistic equations with sign-changing weights and an interior interface-type boundary condition

EBEudes M. BarbozaUniversidade Federal Rural de Pernambuco BMBraulio B. V. MaiaUniversidade Federal Rural da Amazônia OMOlímpio H. MyagakiUniversidade Federal de São Carlos

Key Points

This research aims to investigate the existence of solutions for a class of coupled logistic equations with specific boundary conditions.
Analysis of coupled systems of partial differential equations.
Utilization of the Nehari manifold method for establishing solutions.
Inclusion of an interior interface-type boundary condition.
Establishment of conditions under which solutions exist for the coupled system.
Demonstration that the interface condition significantly affects the solution's behavior.
Characterization of solutions based on the presence of sign-changing weights.

Abstract

Abstract This paper investigates the existence of solutions for the following class of coupled systems of partial differential equations with an interface condition - Δ ⁢ u i = λ i ⁢ a i ⁢ (x) ⁢ u i + b i ⁢ (x) ⁢ | u i | p i - 2 ⁢ u i in Ω i, ∂ ν ⁡ u i = γ ⁢ (u 2 - u 1) on Σ, ∂ η ⁡ u 2 = 0 on Γ, \{aligned {- u₈&

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