| 1. |
- Basarab-Horwath, Peter, et al.
(författare)
-
Classifying evolution equations
- 2001
-
Ingår i: Nonlinear Analysis. - 0362-546X .- 1873-5215. ; 47:8, s. 5135-5144
-
Tidskriftsartikel (refereegranskat)abstract
- A Lie point symmetry classification of evolution equations in 1+1 time-space dimensions was presented. A combination of the standard Lie algorithm for point symmetry and the equivalence group of the given type of equation was used for the classification. For each canonical evolution the maximal symmetry algebra was calculated and related theorems were proved.
|
|
| 2. |
- Cheng, Yuanji
(författare)
-
Multiple solutions for prescribed boundary value problem
- 2002
-
Ingår i: Nonlinear Analysis. - : Elsevier Science Ltd.. - 0362-546X .- 1873-5215. ; 51:3, s. 537-552
-
Tidskriftsartikel (refereegranskat)abstract
- We, in this paper, consider the semilinear elliptic boundary value problem - ∆u = f(x, u) in Ω and u = g on ∂Ω and the corresponding Bolza problem x'' + ∂V(t, x) =0, x(0)= x0, x(T)= x1, where Ω is a bounded open subset in R^n with C² boundary and g is a given continuous function on the boundary of Ω; and T is the given traveling time, x0,x1 are two fixed points in the state space Rn. Under certain conditions on f and V, we show that the above problems have infinitely many solutions
|
|
| 3. |
- Euler, Marianna, et al.
(författare)
-
n-Dimensional real wave equations and the D’Alembert-Hamilton system
- 2001
-
Ingår i: Nonlinear Analysis. - 0362-546X .- 1873-5215. ; 47:8, s. 5125-5133
-
Tidskriftsartikel (refereegranskat)abstract
- We reduce the nonlinear wave equation □nu = αF[exp(βu)] to ordinary differential equtions and construct exact solutions, by the use of a compatible d'Alembert-Hamilton system. The solutions of these ordinary differential equations, together with the solutions of the corresponding d'Alembert-Hamilton equations, provide a rich class of exact solutions of the multidimensional wave equations. The wave equations are studied in n-dimensional Minkowski space.
|
|
| 4. |
- Euler, Norbert, et al.
(författare)
-
On discrete velocity Boltzmann equations and the Painlevé analysis
- 2001
-
Ingår i: Nonlinear Analysis. - 0362-546X .- 1873-5215. ; 47:2, s. 1407-1412
-
Tidskriftsartikel (refereegranskat)abstract
- The multidimensional Bateman equation is investigated to construct explicit solutions of two discrete velocity Boltzmann equations. The Painleve expansion and the general implicit solution are used to construct the solutions in (1 + 1) and (1 + 2) dimensions, respectively. Both these systems of partial differential equations do not pass the Painleve test for integrability.
|
|
| 5. |
|
|
| 6. |
- Kavallaris, Nikos I., et al.
(författare)
-
Global existence and divergence of critical solutions of a non-local parabolic problem in Ohmic heating process
- 2004
-
Ingår i: Nonlinear Analysis. - : Elsevier. - 0362-546X .- 1873-5215. ; 58:7-8, s. 787-812
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate the behaviour of some critical solutions of a non-local initial-boundary value problem for the equation ut=Δu+λf(u)/(∫Ωf(u)dx)2,Ω⊂RN,N=1,2. Under specific conditions on f, there exists a λ∗ such that for each 0<λ<λ∗ there corresponds a unique steady-state solution and u=u(x,t;λ) is a global in time-bounded solution, which tends to the unique steady-state solution as t→∞ uniformly in x. Whereas for λ⩾λ∗ there is no steady state and if λ>λ∗ then u blows up globally. Here, we show that when (a) N=1,Ω=(−1,1) and f(s)>0,f′(s)<0,s⩾0, or (b) N=2,Ω=B(0,1) and f(s)=e−s, the solution u∗=u(x,t;λ∗) is global in time and diverges in the sense ||u∗(·,t)||∞→∞, as t→∞. Moreover, it is proved that this divergence is global i.e. u∗(x,t)→∞ as t→∞ for all x∈Ω. The asymptotic form of divergence is also discussed for some special cases.
|
|
| 7. |
- Yin, Zhaoyang
(författare)
-
Monotone positive solutions of second-order nonlinear differential equations
- 2003
-
Ingår i: Nonlinear Analysis: Theory, Methods & Applications. - 0362-546X. ; 54:3, s. 391-403
-
Tidskriftsartikel (refereegranskat)abstract
- We obtain an existence theorem for monotone positive solutions of nonlinear second-order ordinary differential equations by using the Schauder-Tikhonov fixed point theorem. The result can also be applied to prove the existence of positive solutions of certain semilinear elliptic equations in R-n (n greater than or equal to 3).
|
|
| 8. |
- Kalisch, Henrik
(författare)
-
A uniqueness result for periodic traveling waves in water of finite depth
- 2004
-
Ingår i: Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier BV. - 0362-546X. ; 58:7-8, s. 779-785
-
Tidskriftsartikel (refereegranskat)abstract
- It is shown that in water of finite depth, the surface profile eta of a periodic traveling wave uniquely determines the corresponding flow in the body of the fluid. This holds for rotational flow as long as the vorticity function gamma(psi) satisfies the condition gamma'(psi) max(xis an element ofR) eta(2)(x) < pi(2). This condition is also shown to be sharp.
|
|
| 9. |
|
|
| 10. |
- Wahlén, Erik
(författare)
-
Positive solutions of second-order differential equations
- 2004
-
Ingår i: Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier BV. - 0362-546X. ; 58:3-4, s. 359-366
-
Tidskriftsartikel (refereegranskat)abstract
- We prove a nonoscillation result for second-order nonlinear ordinary differential equations. An application to the Schrodinger equation is also given. (C) 2004 Elsevier Ltd. All rights reserved.
|
|
