Multi-bump type nodal solutions having a prescribed number of nodal domains : II

We prove for generic Kaluza–Klein metrics that any Laplacian eigenfunction has exactly two nodal domains unless it is invariant under the S 1 action.. We also construct an

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Recently, in Goubet and Ricceri (2019), the nonexistence of nontrivial solutions is shown if either ∂Ω has non-negative mean curvature or Ω is an annulus, also for functions f

In Theorem 5.2, we will show that if Ω is a ball, then the alternative (ii) in Theorem 1.2 must hold, thus the bifurcation from infinity does not occur in this case..

The outline of the paper is as follows. In Section 2, we recall the variational characterization of the problem and we prove Theorem 1 and some useful asymptotic estimates. Then,

Pistoia, On the existence and the profile of nodal solutions of elliptic equations involving critical growth,

Finally, in Section 6 we discuss the construction of other functions K that allows the existence of other type of solutions, namely positive solutions that simultaneously are

Three nodal solutions of singularly perturbed elliptic equations on domains without topology.. Trois solutions nodales d’équations elliptiques avec perturbations singulières dans