نتایج جستجو برای ' Laplacian '

Expression and description of most physical and engineering phenomena such as wave propagation, heat transfer, magnetism, etc. lead to the investigation and equational solution of hyperbolic, parabolic, and elliptic kinds. These equations are from basic topics of boundary value and initial value problems. In this paper, we investigate the problem of quasi-linear boundary: −(|𝑢′ |𝑝−2𝑢′ )′ = 𝜆 𝑓(𝑢) 𝑖𝑛 (0,1) 𝑢(0) = 𝑢(1) = 0 Where p and ƛ are two actual parame...

We investigate a periodic version of the Benjamin-Ono (BO) equation associated with a discrete Laplacian. We find some special solutions to this equation, and calculate the values of the first two integrals of motion I1 and I2 corresponding to these solutions. It is found that there exists a strong resemblance between them and the spectra for the Macdonald q-difference operators. To better understand the connection between these classical and quantum integrable systems, we consider the special d...

We consider the discrete system resulting from mixed finite element approximation of a second-order elliptic boundary value problem with Crouzeix–Raviart non-conforming elements for the vector valued unknown function and piece-wise constants for the scalar valued unknown function. Since the mass matrix corresponding to the vector valued variables is diagonal, these unknowns can be eliminated exactly. Thus, the problem of designing an efficient algorithm for the solution of the resulting al...

In this paper we improve some results on the existence of three solutions for the p(x)-Laplacian equations via an abstract result recently obtained by Ricceri in.

We deal with the existence of solution for the nonlinear elliptic problem {−Δpu = λf (x, u) in Ω, u > 0 in Ω, u(x) = 0 on ∂Ω, where Ω denotes a smooth bounded domain in RN , Δpu := div(| ∇u |p−2 ∇u) with 1 < p < N, is the p-Laplacian operator, f : Ω×(0,∞) → [0,∞) is a suitable function and λ > 0 is a real parameter. The nonlinearity f is allowed to behave like either f ...

Based on a continuation principle, we give some existence results of solutions for the nonlinear problem (φ(u′))′= f (t, u), u(0) = u(T ), u′(0) = u′(T ) involving singular vector φ-Laplacian with φ : B(a) → RN (0 < a ≤ +∞) or φ : RN →B(a) (0 < a < +∞) a homeomorphism under the Hartman-type condition or the modified Hartman-type condition.

This paper, following the theory of partial differential equations on variable exponent Sobolev spaces, is mainly concerned with the p(x)-Laplacian eigenvalue problem with a weight function on RN. The results show that the spectrum of such problems contains a continuous family of eigenvalues.

In this paper, we consider the following nonlinear eigenvalue problems for the p-Laplacian: −div(a(x)|∇u|p−2 ∇u)= λ f (x, u) + μg(x, u) in Rn λ,μ > 0, lim|x|→∞u = 0, where 1 < p < n, λ,μ > 0, a is a measurable bounded function, and f and g are nonlinearities having subcritical growth with respect to u. We prove multiple nontrivial solutions using a recent principle of Ricceri (2009). A regularity result is also estab...

Some existence theorems are obtained for infinitely many periodic solutions for second-order (p,q)-Laplacian differential systems by using a general variational principle due to B. Ricceri.

We establish the existence of three positive solutions of the p-Laplacian problem, which involves a singular nonlinearity. Three solutions are obtained by using the cutoff argument and the three critical points theorem proved by Ricceri (2000) in [15] and Bonanno (2003) in [12], provided the nonlinear term is a (p−1)-sublinear growth at infinity.