2025/03/06 by Sekhar Ghosh, Bhowmick, Souvik, Ghosh, Sekhar · 1 citation
Mathematics · #35J60 #35J92 #35M12 #35R11 #47J30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2503.04361
openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we use the method of invariant sets of descending flows to demonstrate the existence of multiple sign-changing solutions for a class of elliptic problems with zero Dirichlet boundary conditions. By combining Nehari manifold techniques with a constrained variational approach and Brouwer degree theory, we establish the existence of a least-energy sign-changing solution. Furthermore, we prove that the energy of the least energy sign-changing solution is strictly greater than twice the ground state energy. This work extends the celebrated results of Bartsch et~al. [Proc. Lond. Math. Soc. (3), 91(1): 129-152, 2005] and Chang et~al. [Adv. Nonlinear Stud., 19(1): 29-53, 2019] to the mixed local and nonlocal p-Laplace operator, providing a novel contribution even in the case when p=2.