1,721,087 research outputs found
T-minima on convex sets and Mosco-convergence
No full textHalf century ago, Umberto Mosco was the ``relatore di tesi (tesi about the Mosco- convergence) di laurea'' of the first author; a quart of century ago, the first author was the ``relatore di tesi di laurea'' of the second author. The roots of this paper are the Mosco-convergence of convex sets and the minimization of integral functionals of the Calculus of Variations. We consider integral functionals of the type J(v)=∫Ω j(x,Dv)-∫Ω f(x)v(x). We study the existence of T-minima (infinite energy minima) on convex sets of the Sobolev space W01,p(Ω) and the stability of the T-minima under the Mosco-convergence of the convex sets
Bounded positive critical points of some multiple integrals of the Calculus of Variations"
No full textA semilinear system of Schrödinger–Maxwell equations
Full text linkIn this paper we are going to prove existence and regularity results for positive solutions of the following elliptic system: −div(M(x)∇u)+rφur−1=f+φr,−div(M(x)∇φ)+ruφr−1=ur.where Ω is a bounded open subset of RN, M is a bounded, uniformly elliptic matrix, r>1, and f≥0 belongs to some Lebesgue space Lm(Ω), with m≥1. We will also prove the relationships of the solutions of the system with saddle points of the integral functional [Formula presented
Very singular solutions for linear Dirichlet problems with singular convection terms
Full text linkWe study the existence of distributional solutions for the boundary value problems (1.1) and (1.2) if E does not belong to LN, namely [Formula presented], A∈R. The size of A plays an important role: if α(N−2)≤|A
Existence Results for a System of Kirchhoff–Schrödinger–Maxwell Equations
Full text linkIn this paper, we study existence, nonexistence, and properties of solutions for some Kirchhoff–Schrödinger–Maxwell systems as (1.3). The solutions can be seen as saddle points of functionals which are unbounded both from above and from below
A weak minima approach to the study of the existence of saddle points of integral functionals
Full text linkWe study of the existence of saddle points of the functional [Formula presented] defined in (1.1) both in the regular case, i.e., if [Formula presented] belongs to [Formula presented], and in the singular one, i.e., if [Formula presented] belongs to [Formula presented]
A consequence of Djairo’s Lectures on the Ekeland variational principle
Full text linkIn this paper we prove that if a functional has bounded minimum u, then is is possible, using Ekeland’s ε-variational principle, to build a minimizing sequence which is uniformly convergent to u
A nonlinear homotopy between two linear Dirichlet problems
No full textIn this paper we focus on the following problem with nonlinear convection term {-div(M(x)∇u)=-div(u|u|θ-1E(x))+f(x)inΩ,u(x)=0on∂Ω,where Ω is an open bounded domain of RN, with N≥ 3 , M(x) is a uniform elliptic matrix with measurable entries, θ∈ (0 , 1) , E(x)∈(Lr(Ω))N, with r∈ (2 , N) , and f(x) ∈ Lm(Ω) , with m> 1. In particular we study how the relation between the parameters θ and r affects existence and summability of solutions
Erratum: A variational semilinear singular system (Nonlinear Analysis, Theory, Methods and Applications 74 (2011) (3849-3860))
No full textWe correct some details of the paper "A variational semilinear singular system" (Nonlinear Analysis, 74 (2011), 3849-3860). (C) 2014 Published by Elsevier Ltd
Nonlinear parabolic equations: qualitative properties of solutions
No full textPitman Research Notes in Mathematics Serie
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