Search results for "Linear"
showing 10 items of 7165 documents
Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities
2020
We consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical gro…
MR2449047 (2009j:47108) Chermisi, Milena; Martellotti, Anna Fixed point theorems for middle point linear operators in $L^1$. Fixed Point Theory Appl.…
2009
In the paper under review the notion of middle point operator is introduced. The authors prove that for a given nonempty, bounded, $\rho$-closed, convex subset K of L1(μ), where $\rho$ is the metric of the convergence locally in measure, if T from (K, $\rho$) to(K, $\rho$) is a continuous, $\rho$-nonexpansive, middle point linear operator, then T has at least one fixed point in K. To prove the theorem they use results of A. V. Bukhvalov [in Operator theory in function spaces and Banach lattices, 95–112, Birkh¨auser, Basel, 1995; MR1322501 (95m:46123)] and M. Furi and A. Vignoli [Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 195–198; MR0279792 (43 #5513)]. Then they …
ZBL MS 63/6 Satco, Bianca-Renata; Turcu, Corneliu-Octavian Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on t…
2013
The authors prove an existence result for a nonlinear integral equation on time scales under weak topology assumption in the target Banach space. In the setting of vector valued functions on time scales they consider the Henstock-Kurzweil-Pettis $\Delta$-integral which is a kind of Henstock integral recently introduced by Cichon, M. [Commun. Math. Anal. 11 (2011), no. 1, 94�110]. In this framework they show the existence of weakly continuous solutions for an integral equation x(t)= f(t, x(t))+ (HKP)\int_0^t g(t,s,x(s)) \Delta s governed by the sum of two operators: a continuous operator and an integral one. The main tool to get the solutions is a generalization of Krasnosel'skii fixed point…
Recensione: MR3198633 Reviewed Olszowy, Leszek A family of measures of noncompactness in the space L1loc(R+) and its application to some nonlinear Vo…
2014
Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
2020
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.
An equivalent formulation of 0-closed sesquilinear forms
2022
AbstractIn 1970, McIntosh introduced the so-called 0-closed sesquilinear forms and proved a corresponding representation theorem. In this paper, we give a simple equivalent formulation of 0-closed sesquilinear forms. The main underlying idea is to consider minimal pairs of non-negative dominating forms.
Risultati di molteplicità per problemi ai limiti superlineari e asintoticamente lineari
2004
No abstract available
MR3112896 Saichev, Alexander I.; Woyczyński, Wojbor A. Distributions in the physical and engineering sciences. Vol. 2. Linear and nonlinear dynamics …
2014
MR2641584 Joiţa, Maria On extremal covariant completely multi-positive linear maps. Proceedings of the Sixth Congress of Romanian Mathematicians. Vol…
2011
A Lebesgue-type decomposition on one side for sesquilinear forms
2021
Sesquilinear forms which are not necessarily positive may have a dierent behavior, with respect to a positive form, on each side. For this reason a Lebesgue-type decomposition on one side is provided for generic forms satisfying a boundedness condition.