The authors prove an infinite-dimensional version of the generalized Mountain Pass Theorem and apply it to establish existence of at least one solution for a semilinear elliptic system with indefinite weights in R^2.
On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in $\mathbb{R}^2$
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.AP 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
An infinite-dimensional mountain pass theorem with applications to nonlinear elliptic systems
The authors prove an infinite-dimensional version of the generalized Mountain Pass Theorem and apply it to establish existence of at least one solution for a semilinear elliptic system with indefinite weights in R^2.