Opuscula Math. 36, no. 3 (2016), 399-407
http://dx.doi.org/10.7494/OpMath.2016.36.3.399

 
Opuscula Mathematica

Existence theorems of nonlinear asymptotic BVP for a homeomorphism

Katarzyna Szymańska-Dębowska

Abstract. In this work, we are concerned with the existence of solutions for the following \(\varphi\)-Laplacian boundary value problem on the half-line \[(\varphi (x'))' =f(t,x,x'),\quad x(0)=0,\quad x'(\infty)=0,\] where \(f:\mathbb{R}_+\times\mathbb{R}^k\times\mathbb{R}^k\to\mathbb{R}^k\) is continuous. The results are proved using the properties of the Leray-Schauder topological degree.

Keywords: half-line, nonlinear, asymptotic boundary value problem, \(\varphi\)-Laplacian, Leray-Schauder degree.

Mathematics Subject Classification: 34B15, 34B40.

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  • Katarzyna Szymańska-Dębowska
  • Lodz University of Technology, Institute of Mathematics, 90-924 Łódź, ul. Wólczańska 215, Poland
  • Communicated by Giovanni Molica Bisci.
  • Received: 2015-05-22.
  • Accepted: 2015-11-26.
  • Published online: 2016-02-21.
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Cite this article as:
Katarzyna Szymańska-Dębowska, Existence theorems of nonlinear asymptotic BVP for a homeomorphism, Opuscula Math. 36, no. 3 (2016), 399-407, http://dx.doi.org/10.7494/OpMath.2016.36.3.399

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