Three nodal solutions of singularly perturbed elliptic equations on domains without topology

Vˆ arsan initiated and catalyzed the study of singularly perturbed stochastic systems proposing new methods: to use the Lie Algebras generated by the diffusion fields ([9], [10],

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

Specifically, we prove in this paper that any nonnegative solution u of (1.1), (1.2) has to be even in x 1 and, if u ≡ 0 and u is not strictly positive in Ω , the nodal set of u

Wei, On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Canad.. Winter, Multiple boundary peak solutions for some

When the maxima of the ground state approach points in the interior of ∂ N Ω , by the exponential decay of the rescaled solutions the situation is rather similar to the case of

In order to overcome the difficulties related to the presence of the supercritical exponent, we proceed as follows: we modify the nonlinear term | u | p − 2 u in such a way that

This paper is concerned with analyzing their nodal property of multi-bump type sign-changing solutions constructed by Coti Zelati and Rabinowitz [Comm.. In some cases we provide

The condition f being odd in u allows the authors of [3] to use both positive and negative solutions at the same mountain pass level c as basic one-bump solutions which are glued