scholarly journals Nonlinear second order system of Neumann boundary value problems at resonance

1989 ◽  
Vol 2 (3) ◽  
pp. 169-184
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Order System ◽  
Periodic Boundary Value Problems ◽  
At Resonance ◽  
Carathéodory Conditions ◽  
Neumann Boundary Value Problems ◽  
Linear Boundary Value Problem

Let f:[0,π]×ℝN→ℝN, (N≥1) satisfy Caratheodory conditions, e(x)∈L1([0,π];ℝN). This paper studies the system of nonlinear Neumann boundary value problems x″(t)+f(t,x(t))=e(t), 0<t<π, x′(0)=x′(π)=0. This problem is at resonance since the associated linear boundary value problem x″(t)=λx(t), 0<t<π, x′(0)=x′(π)=0, has λ=0 as an eigenvalue. Asymptotic conditions on the nonlinearity f(t,x(t)) are offered to give existence of solutions for the nonlinear systems. The methods apply to the corresponding system of Lienard-type periodic boundary value problems.

Solutions to Neumann boundary value problems with a generalized 𝑝-Laplacian

2020 ◽  
Vol 27 (4) ◽  
pp. 629-636
Author(s):  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Continuation Theorem ◽  
Mawhin’S Continuation Theorem ◽  
Neumann Boundary Value Problems

AbstractThe purpose of this work is to investigate the existence of solutions for various Neumann boundary value problems associated to the Laplacian-type operators. The main results are obtained using the extension of Mawhin’s continuation theorem.

scholarly journals Saddle point theorem and nonlinear scalar Neumann boundary value problems

1993 ◽  
Vol 55 (3) ◽  
pp. 386-402 ◽  
Author(s):  
M. N. Nkashama
Keyword(s):  
Saddle Point ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Linear Problem ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Saddle Point Theorem ◽  
Carathéodory Conditions ◽  
The One ◽  
Neumann Boundary Value Problems

AbstractWe are concerned with existence results for nonlinear scalar Neumann boundary value problems u″ + g(x, u) = 0, u′(0) = u′(π) = 0 where g(x, u) satisfies Carathéodory conditions and is (possibly) unbounded. On the one hand we only assume that the function (sgn u)g(x, u) is bounded either from above or from below in some function space, and we impose conditions which relate the asymptotic behavior of the function (for¦u¦large) with the first two eigenvalues of the corresponding linear problem (here G(x, u) = is the potential generated by g). On the other hand we consider cases where the function (sgn u)g(x, u) is unbounded. The potential G(x, u) is not necessarily required to satisfy a convexity condition. Our method of proof is variational, we make use of the Saddle Point Theorem.

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

scholarly journals TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 56 (3) ◽  
pp. 245
Author(s):  
Marzena Szajewska ◽  
Agnieszka Tereszkiewicz
Keyword(s):  
Boundary Value Problems ◽  
Special Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Dirichlet Condition ◽  
Two Dimensional ◽  
Neumann Type ◽  
Neumann Boundary Value Problems ◽  
Real Euclidean Space

Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.

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