Multiplicity results for Kirchhoff type elliptic problems with Hardy potential

Existence of Infinitely Many Solutions for Perturbed Kirchhoff Type Elliptic Problems with Hardy Potential

In this article, by using critical point theory, we show the existence of infinitely many weak solutions for a fourth-order Kirchhoff type elliptic problems with Hardy potential.

Multiplicity Results for Perturbed Fourth-order Kirchhoff-type Problems

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...

Solutions for semilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy potential

Let Ω ⊂ RN be a smooth bounded domain such that 0 ∈ Ω , N ≥ 5, 0 ≤ s < 2, 2∗(s) = 2(N−s) N−2 . We prove the existence of nontrivial solutions for the singular critical problem − u − μ u |x |2 = |u| 2∗(s)−2 |x |s u + λu with Dirichlet boundary condition on Ω for all λ > 0 and 0 ≤ μ < ( N−2 2 )2 − ( N+2 N )2. © 2005 Elsevier Ltd. All rights reserved. MSC: 35J60; 35B33

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.