In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves general variable exponent elliptic operator critical growth. Under some suitable conditions on the nonlinearities, establish existence and multiplicity solutions for problem by using concentration-compactness principle Lions exponents mountain pass theor...

We prove the existence of periodic traveling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases hard and soft on-site potentials. In case potentials, we implement a fixed-point theory approach, combining Schauder's theorem contraction mapping principle. This approach enables us to identify ring in energy space nontrivial exist, (norm) thresholds their exi...

Abstract This paper is devoted to the study of existence and multiplicity weak solutions a Hamiltonian integro-differential system. The main tool used theory min–max based on Mountain-Pass theorem. considered system Fredholm type imposed Dirichlet boundary conditions are occurred at integral bounds. Furthermore, we demonstrate some cases in which equivalent with classical

This article considers p(x)-Kirchhoff type problems with Robin boundary conditions. Using the mountain pass theorem, Ekeland's variational principle, and Krasnoselskii's genus theory, we prove that problem has at least two nontrivial weak solutions or infinitely many under some suitable conditions on nonlinearities. The main results improve generalize previous ones introduced in [2,7].

In this paper, we investigate the existence and multiplicity of solutions for a class quasi-linear problems involving fractional differential equations in χ-fractional space Hκ(x)γ,β;χ(Δ). Using Genus Theory, Concentration-Compactness Principle, Mountain Pass Theorem, show that under certain suitable assumptions considered problem has at least k pairs non-trivial solutions.

Abstract In this work, we study the existence of solution for a class semilinear degenerate elliptic equations in whole space involving Grushin operator and nonlinearity that involves Grushin's critical growth exponential growth. The at least one nontrivial weak is done by combining mountain‐pass theorem, Trudinger–Moser inequality, version result due to Lions corresponding weighted Sobolev spa...