arXiv subjects

Ablanvi Songo

Publications and source records attributed to Ablanvi Songo.

6 recordsLinked to original sources

arXiv2026

Linking theorems for multivalued functionals and application to partial differential inclusions

Using the framework of critical point theory for multivalued functionals developed in \cite{Fri}, we establish some linking theorems for such functionals, which generalizes \cite[Theorem 2.11]{Wi}, \cite[Theorem 2.12]{Wi} and \cite[Theorem 2.12]{Fri}. The proofs of our abstract results rely on a general minimax principle for multivalued mappings. As an application, we obtain a nontrivial solution of a semilinear Dirichlet boundary value problem for partial differential inclusions.

math.AP↗

arXiv2025

An infinite-dimensional mountain pass theorem with applications to nonlinear elliptic systems

The purpose of this paper is to establish a critical point theorem, which is an infinite-dimensional generalization of the classical generalized Mountain Pass Theorem of P. H. Rabinowitz \cite[Theorem 5.3]{Ra}. As application, we obtain the existence of at least one solution to a semilinear elliptic systems with indefinite weights in $\mathbb{R}^2$.

math.AP↗

arXiv2025

Existence result for a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities

We establish the existence of at least one solution to a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities, without imposing the Ambrosetti-Rabinowitz condition or any of its refinements. The proof relies on a generalized saddle point theorem due to Colin and the author \cite{CS}.

math.AP↗

arXiv2025

On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$

In this work, we establish a continuous version of the Fountain theorem by using the framework of the weak slope for continuous functionals, which generalizes Theorem 3.6 of Willem \cite{Wi}. Then we present an application to a semilinear problem.

math.AP↗

arXiv2025

A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations

Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this class, we establish a new natural infinite-dimensional linking theorem for strongly indefinite functionals by using the $\tau-$topology of Kryszewski and Szulkin. Our result is a generalization of the classical linking theorem \cite[Theorem 2.21]{Wi}. As an application, we obtain the existence of a nontrivial solution to a system of coupled Poisson equations.

math.AP↗

arXiv2025

An infinite dimensional saddle point theorem and application

By using the $\tau$-topology of Kryszewski and Szulkin, we establish a natural new version of the Saddle Theorem for strongly indefinite functionals. The abstract result will be applied for studying the existence of a nontrivial solution of the strongly indefinite semilinear Schr\"odinger equation where the associated functional is indefinite, that is, the functional is of the form $J(u) = \dfrac{1}{2} \langle Lu, u \rangle - \Psi(u)$ defined on a Hilbert space $X$, where $L : X \to X$ is a self-adjoint operator with negative and positive eigenspace both infinite-dimensional.

math.AP↗