Search results for " Boundary Value Problem"
showing 10 items of 54 documents
Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian
2004
AbstractThis paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93–104].
Multiple solutions for a discrete boundary value problem involving the p-Laplacian.
2008
Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.
On a mixed boundary value problem involving the p-Laplacian
2011
In this paper we prove the existence of infinitely many solutions for a mixed boundary value problem involving the one dimensional p-Laplacian. A result on the existence of three solutions is also established. The approach is based on multiple critical points theorems.
Morse-Smale index theorems for elliptic boundary deformation problems.
2012
AbstractMorse-type index theorems for self-adjoint elliptic second order boundary value problems arise as the second variation of an energy functional corresponding to some variational problem. The celebrated Morse index theorem establishes a precise relation between the Morse index of a geodesic (as critical point of the geodesic action functional) and the number of conjugate points along the curve. Generalization of this theorem to linear elliptic boundary value problems appeared since seventies. (See, for instance, Smale (1965) [12], Uhlenbeck (1973) [15] and Simons (1968) [11] among others.) The aim of this paper is to prove a Morse–Smale index theorem for a second order self-adjoint el…
Generalized dirichlet problem in nonlinear potential theory
1990
The operator extending the classical solution of the Dirichlet problem for the quasilinear elliptic equation divA(x,▽u)=0 akin to thep-Laplace equation is shown to be unique providedA obeys a specific order principle. The Keldych lemma is also generalized to this nonlinear setting.
A geometrical criterion for nonexistence of constant-sign solutions for some third-order two-point boundary value problems
2020
We give a simple geometrical criterion for the nonexistence of constant-sign solutions for a certain type of third-order two-point boundary value problem in terms of the behavior of nonlinearity in the equation. We also provide examples to illustrate the applicability of our results.
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
2016
The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
Optimality of Increasing Stability for an Inverse Boundary Value Problem
2021
In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for the Schrödinger equation. The rigorous justification of increasing stability for the IBVP for the Schrödinger equation were established by Isakov [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and by Isakov et al. [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141]. In [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141], the authors showed that the stability of this IBVP increases …
Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
2016
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
A PDE model for the spatial dynamics of a voles population structured in age
2020
Abstract We prove existence and stability of entropy weak solutions for a macroscopic PDE model for the spatial dynamics of a population of voles structured in age. The model consists of a scalar PDE depending on time, t , age, a , and space x = ( x 1 , x 2 ) , supplemented with a non-local boundary condition at a = 0 . The flux is linear with constant coefficient in the age direction but contains a non-local term in the space directions. Also, the equation contains a term of second order in the space variables only. Existence of solutions is established by compensated compactness, see Panov (2009), and we prove stability by a doubling of variables type argument.