Author
Giovanna Cerami
Bio: Giovanna Cerami is an academic researcher from Instituto Politécnico Nacional. The author has contributed to research in topics: Scalar field & Type (model theory). The author has an hindex of 14, co-authored 28 publications receiving 2060 citations.
Papers
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TL;DR: In this article, a class of semilinear elliptic Dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results is considered.
1,017 citations
TL;DR: In this article, the existence of positive solutions for the Schrodinger-Poisson system with nonnegative functions has been proved, but not requiring any symmetry property on them and satisfying suitable assumptions.
306 citations
TL;DR: In this article, the authors studied the problem of minimizing the functional complexity of the (1.1) problem on a smooth bounded domain, where 2N 2 < p < 2 < 2 = 2, 2E a + U { 0 }. N.
Abstract: In this paper we are concerned with the following problem: ~ u + 2u = u p ' in g?, u > 0 in 2 , (1.1) u ----0 on 0 Q where ~ Q R ~, N ~ 3, is a smooth bounded domain, and 2N 2 < p < 2 \" = ~ 2 , 2 E a + U { 0 } . N It is well known that problem (1.1) has at least one solution for every p E (2, 2*) and for every 2 E (--22, + co) and that this solution can be found by minimizing the functional e~(u) = f (IVul 2 + ,~u ~) dx D on the manifold
276 citations
199 citations
TL;DR: In this paper, the existence of positive ground and bound state of nonlinear Schrodinger equations was proved using concentration compactness type arguments, and the following results were obtained: −Δu+u=(1+a(x))|u|p−1u+λv,−Δv+v=(1 +b(x)).
112 citations
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Book•
04 Oct 2007
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
Abstract: Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.
935 citations
Book•
01 Mar 2016TL;DR: A thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators can be found in this paper, where the authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of equations, plus their application to various processes arising in the applied sciences.
Abstract: This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
613 citations
TL;DR: In this paper, a nonlinear elliptic problem with fractional powers of the Laplacian operator together with a concave concvex term is studied and the range of parameters for which solutions of the problem exist is characterized.
Abstract: We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave—convex term. We completely characterize the range of parameters for which solutions of the problem exist and prove a multiplicity result. We also prove an associated trace inequality and some Liouville-type results.
460 citations
TL;DR: In this paper, the authors studied the effect of lower order perturbations in the existence of positive solutions to the critical elliptic problem involving the fractional Laplacian.
411 citations