WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Energy Estimates and Existence Results for a Mixed Boundary Value Problem for a Complete Sturm-Liouville Equation Exploiting a Local Minimization Principle
Authors: , ,
Abstract: In our work, we are going to look for local minima for the Euler functional corresponding to a mixed
boundary value problem for a complete Sturm-Liouville equation where the coefficients can also be negative, to
obtain the existence results and energy estimates for solutions for the problem. In particular, we establish the
existence of a non-zero solution for a specific localization of the parameter and show that the solution exists for
positive values of the parameter, under the condition that the nonlinear component exhibits sublinearity both at the
origin and at infinity. The proof relies on a local minimum theorem for differentiable functionals. We also consider
the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz.
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Pages: 220-230
DOI: 10.37394/23206.2025.24.22