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In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation ${(φ_{p} (u^{'}))}^{'} + q (t) f (u) = 0$ , $0 < t < 1$ , where $φ_{p} (s) : = {| s |}^{p - 2} s$ , $p > 1$ , subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient $q (t)$ may be singular at $t = 0, 1$ .

Existence and L∞ estimates of some Mountain-Pass type solutions

José Maria Gomes (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the existence of a positive solution to the BVP ${(Φ (t) u^{'} (t))}^{'} = f (t, u (t)), u^{'} (0) = u (1) = 0,$ imposing some conditions on Φ and f. In particular, we assume $Φ (t) f (t, u)$ to be decreasing in t. Our method combines variational and topological arguments and can be applied to some elliptic problems in annular domains. An $L_{\infty}$ bound for the solution is provided by the $L_{\infty}$ norm of any test function with negative energy.

Existence and location result for the bending of a single elastic beam

Minhós, F., Gyulov, T., Santos, A. I. (2007)

Proceedings of Equadiff 11

Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem.

Malaguti, Luisa, Marcelli, Cristina (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and multiplicity of positive solutions existence and multiplicity of positive solutions time scales.

Pang, Yuanyuan, Bai, Zhanbing (2010)

The Journal of Nonlinear Sciences and its Applications

Existence and multiplicity of positive solutions of a boundary-value problem for sixth-order ODE with three parameters.

Zhang, Liyuan, An, Yukun (2010)

Boundary Value Problems [electronic only]

Existence and multiplicity results for singular $φ$ -Laplacian BVPs on the positive half-line.

Djebali, Smail, Mebarki, Karima (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and nonexistence results for second-order Neumann boundary value problem.

Wang, F., Cui, Y., Zhang, F. (2009)

Surveys in Mathematics and its Applications

Existence and positivity of solutions for a nonlinear periodic differential equation

Ernest Yankson (2012)

Archivum Mathematicum

We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.

Existence and uniqueness of a positive solution for a third-order three-point boundary-value problem.

Palamides, Alex P., Stavrakakis, Nikolaos M. (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales.

Han, Wei, Kao, Yonggui (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and uniqueness of positive solution for a singular nonlinear second-order $m$ -point boundary value problem.

Lv, Xuezhe, Pei, Minghe (2010)

Boundary Value Problems [electronic only]

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