Search results for "solution"
showing 10 items of 5638 documents
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.
Multiplicity theorems for the Dirichlet problem involving the p-Laplacian
2003
Multiplicity theorems for the Dirichlet problem involving the p-Laplacian were proved using variational approach. It was shown that there existed an open interval and a positive real number, and each problem admits at least three weak solutions. Results on the existence of at least three weak solutions for the Dirichlet problems were established.
Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations
2019
We consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations.
Stability of Hamiltonian Systems of Two Degrees of Freedom and of Formally Conservative Mappings Near a Singular Point
1985
We restrict ourselves to the stability problems considered in our lecture because the length of this paper is limited. In contrast to the lecture, however, we consider here not only area preserving mappings but a more general class of mappings.
Characteristic numbers of non‐autonomous emden‐fowler type equations
2006
We consider the Emden‐Fowler equation x” = ‐q(t)|x|2εx, ε > 0, in the interval [a,b]. The coefficient q(t) is a positive valued continuous function. The Nehari characteristic number An associated with the Emden‐Fowler equation coincides with a minimal value of the functional [] over all solutions of the boundary value problem x” = ‐q(t)|x|2εx, x(a) = x(b) = 0, x(t) has exactly (n ‐ 1) zeros in (a, b). The respective solution is called the Nehari solution. We construct an example which shows that the Nehari extremal problem may have more than one solution. First Published Online: 14 Oct 2010
OBSTACLE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS WITH NONHOMOGENEOUS NONLINEAR BOUNDARY CONDITIONS
2008
In this paper we study the questions of existence and uniqueness of solutions for equations of type - div a(x,Du) + γ(u) ∋ ϕ, posed in an open bounded subset Ω of ℝN, with nonlinear boundary conditions of the form a(x,Du) · η + β(u) ∋ ψ. The nonlinear elliptic operator div a(x,Du) modeled on the p-Laplacian operator Δp(u) = div (|Du|p-2Du), with p > 1, γ and β maximal monotone graphs in ℝ2 such that 0 ∈ γ(0) ∩ β(0), [Formula: see text] and the data ϕ ∈ L1(Ω) and ψ ∈ L1(∂ Ω). Since D(γ) ≠ ℝ, we are dealing with obstacle problems. For this kind of problems the existence of weak solution, in the usual sense, fails to be true for nonhomogeneous boundary conditions, so a new concept of solut…
Extended pseudo-fermions from non commutative bosons
2013
We consider some modifications of the two dimensional canonical commutation relations, leading to {\em non commutative bosons} and we show how biorthogonal bases of the Hilbert space of the system can be obtained out of them. Our construction extends those recently introduced by one of us (FB), modifying the canonical anticommutation relations. We also briefly discuss how bicoherent states, producing a resolution of the identity, can be defined.
A New Extension of Darbo's Fixed Point Theorem Using Relatively Meir-Keeler Condensing Operators
2018
We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.
A DUALITY APPROACH TO THE FRACTIONAL LAPLACIAN WITH MEASURE DATA
2011
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like $$(-\Delta)^s v = \mu \quad \text{in } \mathbb{R}^N,$$ ¶ with vanishing conditions at infinity. Here $\mu$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(\Delta)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$.
Landesman-Lazer type (p, q)-equations with Neumann condition
2020
We consider a Neumann problem driven by the (p, q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.