Advances in Differential Equations

Boundary-value problems with non-surjective $\phi$-Laplacian and one-sided bounded nonlinearity

C. Bereanu and J. Mawhin

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Using Leray-Schauder degree theory we obtain various existence results for nonlinear boundary-value problems \begin{eqnarray*} (\phi(u'))'=f(t, u, u'),\quad l(u, u')=0 \end{eqnarray*} where $l(u, u')=0$ denotes the periodic, Neumann or Dirichlet boundary conditions on $[0,T],$ $\phi:\mathbb{R}\rightarrow (-a,a)$ is a homeomorphism, $\phi(0)=0.$

Article information

Adv. Differential Equations, Volume 11, Number 1 (2006), 35-60.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B15: Nonlinear boundary value problems
Secondary: 34C25: Periodic solutions 35J60: Nonlinear elliptic equations 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25] 47N20: Applications to differential and integral equations


Bereanu, C.; Mawhin, J. Boundary-value problems with non-surjective $\phi$-Laplacian and one-sided bounded nonlinearity. Adv. Differential Equations 11 (2006), no. 1, 35--60.

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