This book is a compilation of research studies the authors undertook over many years. The
overall goal of the presented methods is to gain information, in particular existence …

We consider positive solutions of a fractional Lane–Emden-type problem in a bounded
domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the …

In this paper, we study standing wave solutions of the nonlinear Schrödinger equation
(NLS){i∂∂ t++|| p− 1= 0,(t, x)∈× B1,(t, x)= 0,(t, x)∈×∂ B1 (1-1) with B1 the unitary ball of N …

Relying on bifurcation type arguments, we obtain threshold results for the existence, non-
existence and multiplicity of positive solutions with prescribed L 2 norm for the semi-linear …

We prove the uniqueness and nondegeneracy of least energy solutions of a fractional
Dirichlet semilinear problem in any ball and in more general sufficiently large symmetric …

This book provides an introduction to the bifurcation theory approach to global solution
curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems …

In this paper, we investigate a Kirchhoff type elliptic problem, where Ω⊂ ℝ3 is an open ball,
λ∈ ℝ and b≥ 0. We give an extension of the result by Brezis-Nirenberg in 1983 to the case …

In this paper, we are interested in the following degenerate elliptic Monge–Ampère
equation: Under suitable structure conditions on, we can show that and the solutions of …

Starting with the famous article [A. Gidas, WM Ni, L. Nirenberg, Symmetry and related
properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209–243], many papers …

Two results on the existence and uniqueness for the p (x)‐Laplacian‐Dirichlet problem− div
(|∇ u| p (x)− 2∇ u)= f (x, u) in Ω, u= 0 on∂ Ω, are obtained. The first one deals with the case …