Infinitely many solutions for indefinite Kirchhoff equations and Schrodinger-Poisson systems

Article Mathematics, Applied

Sufficient and necessary conditions for ground state sign-changing solutions to the Schrodinger-Poisson system with cubic nonlinearity on bounded domains

Shubin Yu et al.

Summary: This paper investigates the existence of ground state sign-changing solutions in the Schrodinger-Poisson system, improving upon recent results by Khoutir (2021). Omega is a bounded smooth domain in R-3, with mu > 0 and lambda > 0.

APPLIED MATHEMATICS LETTERS (2022)

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Article Physics, Multidisciplinary

A Critical Concave-Convex Kirchhoff-Type Equation in R4 Involving Potentials Which May Vanish at Infinity

Marcelo C. Ferreira et al.

Summary: In this study, we investigate the existence and multiplicity of solutions for a Kirchhoff-type problem in R-4 with critical and concave-convex nonlinearity. The tie between the growth of the nonlocal term and the critical nonlinearity poses a challenge in the variational analysis. Main tools used include the mountain-pass and Ekeland's theorems, Lions' Concentration Compactness Principle, and an extension to RN of the Struwe's global compactness theorem.

ANNALES HENRI POINCARE (2022)

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Article Mathematics, Applied

On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension

F. Faraci et al.

Summary: The paper addresses a parametrized Kirchhoff type problem involving a critical nonlinearity in high dimension, examining the existence, nonexistence, and multiplicity of solutions under a subcritical perturbation. Variational properties and analysis of the fiber maps of the associated energy functional are utilized. The study extends to a wider range of parameters through the investigation of Nehari manifolds.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2021)

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Article Mathematics, Applied

Nodal solutions for Schrodinger-Poisson systems with concave-convex nonlinearities

Zhen-Li Yang et al.

Summary: In this paper, the existence of nodal solutions for a class of Schrödinger-Poisson systems is studied. The proof relies on constrained variational method and quantitative deformation lemma, showing the existence of a nodal solution with positive energy for lambda values satisfying certain conditions.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

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Article Mathematics, Applied