1,721,004 research outputs found
Non-existence results for the coupled Klein-Gordon-Maxwell equations
Get PDFKlein-Gordon-Maxwell system; Schrödinger-Maxwell system; non-existence; bound state
Optimal solvability for the fractional p-Laplacian with Dirichlet conditions
No full textWe study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a (p-1)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald [7] and Diaz-Saa [11] to the nonlinear nonlocal framework
Control of degenerate and singular parabolic equations: Carleman estimates and observability
No full textThis book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area
Asymptotically critical points and their multiplicity
No full textIn this paper we study multiplicity results for the critical points of
a functional via topological information which ensures multiplicity of
critical points for a sequence of approximating functionals. The main
statement is quite simple, and it seems it could be usefully compared
with a large class of problems. In particular we mention some problems
that can be studied in this framework
Asymptotical Multiplicity and some reversed variational inequalities
No full textWe are concerned with multiplicity results for solutions of some
reversed variational inequalities, in which the inequality is opposite
with respect to the classical inequalities introduced by Lions and
Stampacchia. The inequalities we study arise from a family
(P) of elliptic problems of the fourth order when
tends to . We use two basic tools: the -theorems and
a theorem about the multiplicity of ``asymptotically critical''
points. In the last section some open problems are listed
Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions
Get PDFWe consider a boundary value problem driven by the p-fractional Laplacian with nonlocal Robin boundary conditions and we provide necessary and sufficient conditions which ensure the existence of a unique positive (weak) solution. The results proved in this paper can be considered a first step towards a complete generalization of the classical result by Brezis and Oswald (Nonlinear Anal 10:55–64, 1986) to the nonlocal setting
An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems
Get PDFWe prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appears in models describing the propagation of flames. A careful adaptation of well known variational methods is required to deal with the possible existence of negative eigenvalues
A Brezis-Oswald approach for mixed local and nonlocal operators
Get PDFIn this paper, we provide necessary and sufficient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasilinear local and a nonlocal operator, i.e.L-p,L-s = -Delta(p) + (-Delta)(p)(s).Our main result is resemblant to the celebrated work by Brezis-Oswald [Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986) 55-64]. In addition, we prove a regularity result of independent interest
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