In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.
A class of perturbed fractional nonlinear systems is studied. The dynamical system possesses two control parameters and a Lipschitz nonlinearity order of $p-1$
p
−
1
. The multiplicity of the weak solutions is proved by means of the variational method and by Ricceri critical points theorems. An illustrative example is analyzed in order to highlight the obtained result.
The paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. In addition, we establish the blow-up of solutions with nonpositive initial energy.
In this paper, the existence of multiplicity distinct weak solutions is proved for differentiable functionals for perturbed systems of impulsive nonlinear fractional differential equations. Further, examples are given to show the feasibility and efficacy of the key findings. This work is an extension of the previous works to Banach space.
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