Search results for "Nonlinear boundary value problem"
showing 9 items of 9 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].
Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian
2017
Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.
Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type
2021
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
Numerische Behandlung von Verzweigungsproblemen bei gew�hnlichen Differentialgleichungen
1979
We present a new method for the numerical solution of bifurcation problems for ordinary differential equations. It is based on a modification of the classical Ljapunov-Schmidt-theory. We transform the problem of determining the nontrivial branch bifurcating from the trivial solution into the problem of solving regular nonlinear boundary value problems, which can be treated numerically by standard methods (multiple shooting, difference methods).
Multiplicity of solutions to a nonlinear boundary value problem of concave–convex type
2015
Abstract Problem (P) { − Δ p u + | u | p − 2 u = | u | r − 1 u x ∈ Ω | ∇ u | p − 2 ∂ u ∂ ν = λ | u | s − 1 u x ∈ ∂ Ω , where Ω ⊂ R N is a bounded smooth domain, ν is the unit outward normal at ∂ Ω , Δ p is the p -Laplacian operator and λ > 0 is a parameter, was studied in Sabina de Lis (2011) and Sabina de Lis and Segura de Leon (in press). Among other features, it was shown there that when exponents lie in the regime 1 s p r , a minimal positive solution exists if 0 λ ≤ Λ , for a certain finite Λ , while no positive solutions exist in the complementary range λ > Λ . Furthermore, in the radially symmetric case a second positive solution exists for λ varying in the same full range ( 0 , Λ ) …
Types and Multiplicity of Solutions to Sturm–Liouville Boundary Value Problem
2015
We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.
Green’s function and existence of solutions for a third-order three-point boundary value problem
2019
The solutions of third-order three-point boundary value problem x‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η), where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.
Nonlocal Third Order Boundary Value Problems with Solutions that Change Sign
2014
We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.
Two-Dimensional Differential Systems with Asymmetric Principal Part
2013
We consider the Sturm–Liouville nonlinear boundary value problem $$\displaystyle\begin{array}{rcl} \left \{\begin{array}{l} x^{\prime} = f(t,y) + u(t,x,y),\\ y^{\prime} = -g(t, x) + v(t, x, y), \end{array} \right.& & {}\\ \begin{array}{l} x(0)\cos \alpha - y(0)\sin \alpha = 0,\\ x(1)\cos \beta - y(1)\sin \beta = 0, \end{array} & & {}\\ \end{array}$$ assuming that the limits \(\lim _{y\rightarrow \pm \infty }\frac{f(t,y)} {y} = f_{\pm }\), \(\lim _{x\rightarrow \pm \infty }\frac{g(t,x)} {x} = g_{\pm }\) exist. Nonlinearities u and v are bounded. The system includes various cases of asymmetric equations (such as the Fucik one). Two classes of multiplicity results are discussed. The first one …