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In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = up, p > 1, or f(u) = λu + a1up1 + ... + akupk, with pj > 1, aj > 0 for j = 1, ..., k and 0 ≤ λ < μ12 where μ1 = π2/4R2.

Uniqueness of solutions for fourth-order nonlocal boundary value problems.

Henderson, Johnny, Ma, Ding (2006)

Boundary Value Problems [electronic only]

Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.

Jesús Ildefonso Díaz, José Evaristo Saa (1992)

Publicacions Matemàtiques

We show the uniqueness of the very singular self-similar solution of the equationut - Δ pum + uq = 0.The result is carried out by studying the stationary associate equation and by introducing a suitable change of unknown. That allows to assume the zero-order perturbation term in the new equation to be monotone increasing. A careful study of the behaviour of solutions near the boundary of their support is also used in order to prove the main result.

Upper and lower solutions for a second-order three-point singular boundary-value problem.

Zhang, Qiumei, Jiang, Daqing, Weng, Shiyou, Gao, Haiyin (2009)

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

Upper and lower solutions for first order problems with nonlinear boundary conditions.

Daniel Franco, Juan J. Nieto, Donal O'Regan (2003)

Extracta Mathematicae

Upper and lower solutions for singularly perturbed semilinear Neumann's problem

Róbert Vrábeľ (1997)

Mathematica Bohemica

The paper establishes sufficient conditions for the existence of solutions of Neumann’s problem for the differential equation $μ y " + k y = f (t, y)$ which tend to the solution of the reduced problem $k y = f (t, y)$ on $[0, 1]$ as $μ \to 0 .$

Upper and lower solutions method and a fractional differential equation boundary value problem.

Shi, Ailing, Zhang, Shuqin (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Upper and lower solutions method for a class of singular fractional boundary value problems with $p$ -Laplacian operator.

Wang, Jinhua, Xiang, Hongjun (2010)

Abstract and Applied Analysis

Upper and lower solutions satisfying the inverse inequality

Irena Rachůnková (1997)

Annales Polonici Mathematici

We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.

Upper bounds for the eigenvalues of differential equations.

Karaa, Samir (2006)

Journal of Inequalities and Applications [electronic only]

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