There has been an increasing interest in recent years to develop theories and techniques by which one can obtain much more information and property on the critical points of the differentiable functions. Since there are plenty of results on the existence of solutions to elliptic equations in the past decades, when we study the partial differential equations of elliptic type, a rather natural question is “Can we say more on the profile of the solutions except for the existence obtained before?” One of the important aspects in this direction is the so-called sign-changing solutions to nonlinear elliptic equations. It has attracted much attention in the last twenty years. Finding sign-changing solutions and studying their richer structure are themselves of interest to many pure mathematicians. In fact, the existence of sign-changing solutions to many elliptic equations, including some Schrödinger equations from physics and some critical Sobolev exponent equations from differential geometry, has not been adequately settled and is very challenging.

We invite authors to present original research articles as well as review articles in the existence of sign-changing solutions and further properties to miscellaneous elliptic equations and systems. The special issue will become an international forum for researches to present the most recent developments and ideas in the field. The topics to be covered include, but are not limited to:

• Sign-changing solutions to Dirichlet boundary value problems
• Sign-changing solutions to pure critical exponent problems
• Sign-changing solutions to Schrödinger equations
• Sign-changing solutions to higher order elliptic equations
• Sign-changing solutions to elliptic equations with perturbation from symmetry
• Sign-changing solutions to elliptic systems
• Symmetry results for sign-changing solutions
• The least energy nodal solutions and their properties
• Estimates on the number of nodal domains
• Sign-changing solutions to singularly perturbed equations
• Morse index on sign-changing solutions