Search results for "VARIATION"
showing 10 items of 2124 documents
An Henstock-Kurzweil type integral on a meausure metric space
2014
We consider an Henstock-Kurzweil type integral defined on a complete measure metric space $X=(X, d)$ endowed with a Radon measure $\mu$ and with a family $\F$ of ``intervals" that satisfies, besides usual conditions, the Vitali covering theorem. In particular, for such integral, we obtain extensions of the descriptive characterization of the classical Henstock-Kurzweil integral on the real line, in terms of $ACG_*$ functions and in terms of variational measures. Moreover we show that, besides the usual Henstock-Kurzweil integral on the real line, such integral includes also the dyadic Henstock-Kurzweil integral, the $GP$-integral and the $s$-HK integral. For this last integral we prove a be…
Existence of two positive solutions for anisotropic nonlinear elliptic equations
2021
This paper deals with the existence of nontrivial solutions for a class of nonlinear elliptic equations driven by an anisotropic Laplacian operator. In particular, the existence of two nontrivial solutions is obtained, adapting a two critical point results to a suitable functional framework that involves the anisotropic Sobolev spaces.
MR3058477 Reviewed Ereú, Thomás; Sánchez, José L.; Merentes, Nelson; Wróbel, Małgorzata Uniformly continuous set-valued composition operators in the …
2011
In this paper it is established a property of a composition operator between spaces of functions of bounded variation in the sense of Schramm. Let X and Y be two real normed spaces, C a convex cone in X and I a closed bounded interval of the real line. Moreover let cc(Y) be the family of all non-empty closed convex and compact subsets of Y. The authors study the Nemytskij (composition) operator (HF)(t)=h(t,F(t)), where F: I \rightarrow C and h: I\times C \rightarrow cc(Y) is a given set-valued function. They show that if the Nemytskij operator $H$ is uniformly continuous and maps the space \Phi BV (I;C) of functions (from I to C) of bounded \Phi-variation in the sense of Schramm into the sp…
Existence and multiplicity of solutions for non linear elliptic Dirichlet systems
2012
The existence and multiplicity of solutions for systems of nonlinear elliptic equations with Dirichlet boundary conditions is investigated. Under suitable assumptions on the potential of the nonlinearity, the existence of one, or two, or three solutions is established. Our approach is based on variational methods.
A variational henstock integral characterization of the radon-nikodým property
2009
A characterization of Banach spaces possessing the Radon-Nikodym property is given in terms of finitely additive interval functions. We prove that a Banach space X has the RNP if and only if each X-valued finitely additive interval function possessing absolutely continuous variational measure is a variational Henstock integral of an X-valued function. Due to that characterization several X-valued set functions that are only finitely additive can be represented as integrals.
Ordinary (p_1,...,p_m)-Laplacian system with mixed boundary value
2016
In this paper we prove the existence of multiple weak solutions for an ordinary mixed boundary value system with (p_1,...,p_m)-Laplacian by using recent results of critical points.
MR2819034 Castillo, René Erlín The Nemytskii operator on bounded p-variation in the mean spaces. Mat. Enseñ. Univ. (N. S.) 19 (2011), no. 1, 31–41. (…
2012
The author introduces the notion of bounded $p$-variation in the sense of $L_p$-norm. Precisely: Let $f \in L_p[0,2\pi]$ with $1<p<\infty$. Let $P: 0=t_0 <t_1< \cdots <t_n=2\pi$ be a partion of $[0,2\pi]$ if $$V_p^m(f,T) = \sup \{\sum_{k=1} ^{n}\int_T\frac{|f(x+t_k)-f(x+t_{k-1})|^p)}{|t_k-t_{k-1}|^{p-1}}\}< \infty,$$ where the supremum is taken over all partitions $P$ of $[0,2\pi]$ and $T=\mathbb{R}/2\pi \mathbb{Z}$, then $f$ is said to be of bounded $p$-variation in the mean. The author obtains a Riesz type result for functions of bounded $p$-variation in the mean and gives some properties for functions of bounded $p$-variation by using the Nemytskii operator.
MR2789279 Aziz, Wadie; Leiva, Hugo; Merentes, Nelson; Rzepka, Beata A representation theorem for φ-bounded variation of functions in the sense of Rie…
2012
The authors consider the class $V_\varphi^R (I^b_a)$ of functions $f:I^b_a =[a_1,b_1]\times [a_2,b_2]\subset \mathbb{R}^2 \to \mathbb{R}$ with bounded $\varphi$-total variation in the sense of Riesz, where $\varphi: [0,+ \infty) \to [0,+ \infty)$ is nondecreasing and continuous with $\varphi(0)=0$ and $\varphi(t) \to +\infty$ as $t \to +\infty$. If we assume that $\varphi$ is also such that $\lim_{t \to +\infty}\frac{\varphi(t)}{t}= +\infty$, then we obtain the main result. Precisely, the authors give a characterization of function of two variables defined on a rectangle $I^b_a$ belonging to $V_\varphi^R (I^b_a)$. Clearly, this result is a generalization of the Riesz Lemma.
MR2664252 Aziz, W.; Leiva, H.; Merentes, N.; Sánchez, J. L. Functions of two variables with bounded φ-variation in the sense of Riesz. J. Math. Appl.…
2011
The authors consider the space $BV_\varphi^R (I^b_a,\mathbb{R})$ of functions $f:I^b_a =[a,b]\times [a,b]\subset \mathbb{R}^2 \to \mathbb{R}$ with a $\varphi$-bounded variation in the sense of Riesz, where $\varphi: [0,+ \infty) \to [0,+ \infty)$ is nondecreasing and continuous with $\varphi(0)=0$ and $\varphi(t) \to +\infty$ as $t \to +\infty$. The authors show that $BV_\varphi^R (I^b_a,\mathbb{R})$ is a Banach algebra. Let $h: I^b_a \times \mathbb{R} \to \mathbb{R}$ and let $H: \mathbb{R}^{I^b_a} \to \mathbb{R}$ be the composition operator associated to $h$, that is the operator defined by $(Hf)(x)= h(x, f(x))$ for each $x \in I^b_a$. Then the authors consider the problem of characterizin…
Genetic variation in human leukocyte antigen and susceptibility to acute myeloid leukemia.
2015
In this issue of Acta Haematologica, Authors report the association between the Human Major Histocompatibility complex (MHC) HLA-C3 and Acute Myeloid Leukemia (AML) in Korean population, confirming previous studies on association between HLA-C and AML.