86,597 research outputs found
Least energy solutions to the Dirichlet problem for the equation −D(u) = f (x, u)
No full textLet be a bounded smooth domain in RN. We prove a general
existence result of least energy solutions and least energy nodal ones
for the problem −u = f(x, u) in u = 0 on ∂ (P) where f is a Carathéodory function. Our result includes some previous results related to special cases of f . Finally, we propose some open questions concerning the global minima of the restriction on the Nehari manifold of the energy functional associated with (P) when the nonlinearity is of the type f(x, u) = λ|u| s−2u − μ|u| r−2u, with s, r ∈ (1, 2) and λ,μ > 0
Absolutely continuous variational measures of Mawhin's type
No full textIn this paper we study absolutely continuous and σ-finite variational
measures corresponding to Mawhin, F- and BV -integrals. We obtain
characterization of these σ-finite variational measures similar to those obtained
in the case of standard variational measures. We also give a new proof of the
Radon-Nikod ́ym theorem for these measures
Existence and multiplicity of solutions for Dirichlet problems involving nonlinearities with arbitrary growth.
No full textIn this article we study the existence and multiplicity of solutions for the Dirichlet problem
\displaylines{ -\Delta_p u=\lambda f(x,u)+ \mu g(x,u)\quad\hbox{in }\Omega,\cr
u=0\quad\hbox{on } \partial \Omega}
where is a bounded domain in , are Caratheodory functions, and are nonnegative parameters. We impose no growth condition at on the nonlinearities f,g. A corollary to our main result improves an existence result recently obtained by Bonanno via a critical point theorem for functionals which do not satisfy the usual sequential weak lower semicontinuity property
Regularity of some method of summation for double sequences
No full textSome generalization of Toeplitz method of summation is introduced for double sequences and condition of regularity of it is obtained.<br /
Henstock-Kurzweil type integrals on zero-dimensional groups and its application in Harmonic Analysis
No full textWe introduce here a Henstock type integral on compact subsets of a locally compact zero-dimensional abelian group and we use this integral to solve the problem of recovering the coefficients of convergent series with respect to characters of a compact zero dimensional abelian group and to obtain an inversion formula for multiplicative integral transform with a kernel expressed in terms of characters of a locally compact zero dimensional abelian group
Multidimensional P-adic Integrals in some Problems of Harmonic Analysis
No full textThe paper is a survey of results related to the problem of recovering the coefficients of some classical orthogonal series from their sums by generalized Fourier formulas. The method is based on reducing the coefficient problem to the one of recovering a function from its derivative with respect to an appropriate derivation basis. In the case of the multiple Vilenkin system the problem is solved by using a multidimensional P-adic integral
On the possible values of upper and lower derivatives with respect to differentiation bases of product structure.
No full textA solution of the Guzmán's problem on possible values of upper and lower derivatives
is given for the class of translation invariant and product type differentiation bases formed by ndimensional
intervals. Namely, the bases from the mentioned class are characterized, for which
integral means of a summable function can boundedly diverge only on a set of zero measur
A version of Hake's theorem for Kurzweil-Henstock integral in terms of variational measure
No full textWe introduce the notion of variational measure with respect to a derivation basis in a topological measure space and consider a Kurzweil-Henstock-type integral related to this basis. We prove a version of Hake's theorem in terms of a variational measure
Dual of the Class of HKr Integrable Functions
No full textWe define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space
On Descriptive Characterizations of an Integral Recovering a Function from Its -Derivative
No full textThe notion of Lr-variational measure generated by a function F ∈ Lr[a, b] is introduced and, in terms of absolute continuity of this measure, a descriptive characterization of the HKr -integral recovering a function from its Lr-derivative is given. It is shown that the class of functions generating absolutely continuous Lr-variational measure coincides with the class of ACGr -functions which was introduced earlier, and that both classes coincide with the class of the indefinite HKr-integrals under the assumption of Lr-differentiability almost everywhere of the functions consisting these classe
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