Search results for "Linear"
showing 10 items of 7165 documents
Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems
1993
IN THIS PAPER we study: (i) a class of operator equations in an abstract Hilbert space; and (ii) the L2-theory of certain nonlinear Schrodinger equations which can be viewed as special cases of (i). In order to describe the type of abstract nonlinear eigenvalue problems to be discussed, consider a real Hilbert space H with scalar product (* , *) and norm II.11 and let S be a (not necessarily bounded) positive self-adjoint linear operator in li. We write S in the form
Fixed point methods and accretivity for perturbed nonlinear equations in Banach spaces
2020
Abstract In this paper we use fixed point theorems to guarantee the existence of solutions for inclusions of the form A u + λ u + F u ∋ g , where A is a quasi-m-accretive operator defined in a Banach space, λ > 0 , and the nonlinear perturbation F satisfies some suitable conditions. We apply the obtained results, among other things, to guarantee the existence of solutions of boundary value problems of the type − Δ ρ ( u ( x ) ) + λ u ( x ) + F u ( x ) = g ( x ) , x ∈ Ω , and ρ ( u ) = 0 on ∂Ω, where the Laplace operator Δ should be understood in the sense of distributions over Ω and to study the existence and uniqueness of solution for a nonlinear integro-differential equation posed in L 1 …
Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities
2022
Abstract We consider positive critical points of Caffarelli–Kohn–Nirenberg inequalities and prove a Liouville type result which allows us to give a complete classification of the solutions in a certain range of parameters, providing a symmetry result for positive solutions. The governing operator is a weighted p -Laplace operator, which we consider for a general p ∈ ( 1 , d ) . For p = 2 , the symmetry breaking region for extremals of Caffarelli–Kohn–Nirenberg inequalities was completely characterized in Dolbeault et al. (2016). Our results extend this result to a general p and are optimal in some cases.
Nonlinear vector Duffing inclusions with no growth restriction on the orientor field
2019
We consider nonlinear multivalued Dirichlet Duffing systems. We do not impose any growth condition on the multivalued perturbation. Using tools from the theory of nonlinear operators of monotone type, we prove existence theorems for the convex and the nonconvex problems. Also we show the existence of extremal trajectories and show that such solutions are $C_0^1(T,\mathbb{R}^N)$-dense in the solution set of the convex problem (strong relaxation theorem).
Weak solution for Neumann (p,q)-Laplacian problem on Riemannian manifold
2019
We prove the existence of a nontrivial solution for a nonlinear (p, q)-Laplacian problem with Neumann boundary condition, on a non compact Riemannian manifold. The idea is to reduce the problem in variational form, which means to consider the critical points of the corresponding Euler-Lagrange functional in an Orlicz-Sobolev space. (C) 2019 Elsevier Inc. All rights reserved.
Asymptotic Behaviors of Solutions to quasilinear elliptic Equations with critical Sobolev growth and Hardy potential
2015
Abstract Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations − Δ p u − μ | x | p | u | p − 2 u = Q ( x ) | u | N p N − p − 2 u , x ∈ R N , where 1 p N , 0 ≤ μ ( ( N − p ) / p ) p and Q ∈ L ∞ ( R N ) .
Uniqueness of positive solutions to some nonlinear Neumann problems
2017
Abstract Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem { div ( y a ∇ u ( x , y ) ) = 0 , x ∈ R n , y > 0 , lim y → 0 + y a u y ( x , y ) = − f ( u ( x , 0 ) ) , x ∈ R n , under general nonlinearity assumptions on the function f : R → R for any constant a ∈ ( − 1 , 1 ) .
Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Dislocated Metric Spaces
2013
Common fixed point results for mappings satisfying locally contractive conditions on a closed ball in an ordered complete dislocated metric space have been established. The notion of dominated mappings is applied to approximate the unique solution of nonlinear functional equations. Our results improve several well-known conventional results.
Hamiltonians Generated by Parseval Frames
2021
AbstractIt is known that self-adjoint Hamiltonians with purely discrete eigenvalues can be written as (infinite) linear combination of mutually orthogonal projectors with eigenvalues as coefficients of the expansion. The projectors are defined by the eigenvectors of the Hamiltonians. In some recent papers, this expansion has been extended to the case in which these eigenvectors form a Riesz basis or, more recently, a ${\mathcal{D}}$ D -quasi basis (Bagarello and Bellomonte in J. Phys. A 50:145203, 2017, Bagarello et al. in J. Math. Phys. 59:033506, 2018), rather than an orthonormal basis. Here we discuss what can be done when these sets are replaced by Parseval frames. This interest is moti…
Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series
2015
Abstract The problem of recovering the coefficients of rectangular convergent multiple Haar and Walsh series from their sums, by generalized Fourier formulas, is reduced to the one of recovering a function (the primitive) from its derivative with respect to the appropriate derivation basis. Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals are compared and it is shown that a Perron-type integral, defined by major and minor functions having a special continuity property, solves the coefficients problem for series which are convergent everywhere outside some uniqueness sets.