Multiplicity results for the Kirchhoff type equation via critical groups

Multiplicity Results for Perturbed Fourth-order Kirchhoff-type Problems

Multiplicity result to some Kirchhoff-type biharmonic equation involving exponential growth conditions

In this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎Using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

Multiplicity of Nontrivial Solutions for Kirchhoff Type Problems

Copyright q 2010 Bitao Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. By using variational methods, we study the multiplicity of solutions for Kirchhoff type problems −a b Ω |∇u| 2 Δu f x, u, in Ω; u 0, on ∂Ω. Existe...

MULTIPLICITY RESULTS FOR A CLASS OF p(x)-KIRCHHOFF TYPE EQUATIONS WITH COMBINED NONLINEARITIES

Using the mountain pass theorem combined with the Ekeland variational principle, we obtain at least two distinct, non-trivial weak solutions for a class of p(x)-Kirchhoff type equations with combined nonlinearities. We also show that the similar results can be obtained in the case when the domain has cylindrical symmetry.

multiplicity result to some kirchhoff-type biharmonic equation involving exponential growth conditions

in this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.