Multiple nodal solutions having shared componentwise nodal numbers for coupled Schrödinger equations

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Nodal Solutions of Elliptic Equations with Critical Sobolev Exponents

Nodal solutions to quasilinear elliptic equations on compact Riemannian manifolds

We show the existence of nodal solutions to perturbed quasilinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds. A nonexistence result is also given.

Nodal Curves and Riccati Solutions of Painlevé Equations

In this paper, we study Riccati solutions of Painlevé equations from a view point of geometry of Okamoto-Painlevé pairs (S,Y ). After establishing the correspondence between (rational) nodal curves on S − Y and Riccati solutions, we give the complete classification of the configurations of nodal curves on S − Y for each Okamoto–Painlevé pair (S, Y ). As an application of the classification, we ...

On Nodal Solutions to Generalized Emden-fowler Equations

We introduce a new variational method in order to derive results concerning existence and nodal properties of solutions to superlinear equations, and we focus on applications to the equation where h is a Caratheodory function which is odd in u. In the particular case where h is radially symmetric, we prove, for given n 2 N, the existence of a solution having precisely n nodal domains, whereas s...