Related papers: Nonlinear variational problems with lack of compac…
For a class of second-order discrete Hamiltonian systems $\Delta^2x(t-1)-L(t)x(t)+V'_x(t,x(t))=0$, we investigate the existence of homoclinic orbits by applying variational method, where $L$ and $V(\cdot,x)$ are periodic functions. Further,…
This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory…
In this work, we study the existence and multiplicity of solutions for a class of problems involving the $\phi$-Laplacian operator in a bounded domain, where the nonlinearity has a critical growth. The main tool used is the variational…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
In this article we prove new results regarding the existence and the uniqueness of global variational solutions to Neumann initial-boundary value problems for a class of non-autonomous stochastic parabolic partial differential equations.…
This article deals with a survey of recent developments and results on Choquard equations where we focus on the existence and multiplicity of solutions of the partial differential equations which involve the nonlinearity of convolution…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local…
The present paper studies the existence of weak solutions for the following type of non-homogeneous system of equations \begin{equation*} (S) \left\{\begin{aligned} (-\Delta)^{s_1}_{p_1} u &=u|u|^{\alpha-1}|v|^{\beta+1}+f_1(x) \,\mbox{ in…
Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded…
Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging…
We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type there are two infinite families of T-periodic solutions,…
This paper deals with the lack of compactness in nonlinear elliptic problems $(P)$. In particular, a domain $\Omega$ is provided where not converging Palais-Smale sequences exist at every energy level. Nevertheless, it is proved that…
The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…
In this article, we study a class of fully nonlinear double-divergence systems with free boundaries associated with a minimization problem. The variational structure of Hessian-dependent functional plays a fundamental role in proving the…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the…
The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the Yamabe problem and the corresponding…