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In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones.

Existence of solutions to a third-order multi-point problem on time scales.

Anderson, Douglas R., Hoffacker, Joan (2007)

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

Existence of symmetric positive solutions for an $m$ -point boundary value problem.

Sun, Yongping, Zhang, Xiaoping (2007)

Boundary Value Problems [electronic only]

Existence of three positive solutions for $m$ -point discrete boundary value problems with $p$ -Laplacian.

Guo, Yanping, Wei, Wenying, Chen, Yuerong (2009)

Discrete Dynamics in Nature and Society

Existence of three positive solutions to nonlinear boundary value problems.

Wang, Li, Li, Jianli (2010)

Mathematical Problems in Engineering

Existence of three solutions for a higher-order boundary-value problem.

Graef, John R., Kong, Lingju, Kong, Qingkai (2009)

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

Existence Principles for Singular Vector Nonlocal Boundary Value Problems with $φ$ -Laplacian and their Applications

Staněk, Svatoslav (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Existence principles for solutions of singular differential systems ${(φ (u^{'}))}^{'} = f (t, u, u^{'})$ satisfying nonlocal boundary conditions are stated. Here $φ$ is a homeomorphism $ℝ^{N}$ onto $ℝ^{N}$ and the Carathéodory function $f$ may have singularities in its space variables. Applications of the existence principles are given.

Existence results for higher-order boundary value problems on time scales.

Liu, Jian, Sang, Yanbin (2009)

Advances in Difference Equations [electronic only]

Existence results for singular boundary value problem of nonlinear fractional differential equation.

Cui, Yujun (2011)

Abstract and Applied Analysis

Existence theory for single and multiple solutions to singular positone boundary value problems for the delay one-dimensional p-Laplacian

Daqing Jiang, Xiaojie Xu, Donal O'Regan, Ravi P. Agarwal (2003)

Annales Polonici Mathematici

The existence of single and multiple nonnegative solutions for singular positone boundary value problems to the delay one-dimensional p-Laplacian is discussed. Throughout our nonlinearity f(·,y) may be singular at y = 0.

Explosive solutions of semilinear elliptic systems with gradient term.

Marius Ghergu, Vicentiu Radulescu (2003)

RACSAM

Estudiamos la existencia de soluciones del sistema elíptico no lineal Δu + |∇u| = p(|x|)f(v), Δv + |∇v| = q(|x|)g(u) en Ω que explotan en el borde. Aquí Ω es un dominio acotado de RN o el espacio total. Las nolinealidades f y g son funciones continuas positivas mientras que los potenciales p y q son funciones continuas que satisfacen apropiadas condiciones de crecimiento en el infinito. Demostramos que las soluciones explosivas en el borde dejan de existir si f y g son sublineales. Esto se tiene...

Functions uniformly quiet at zero and existence results for one-parameter boundary value problems

G. L. Karakostas, P. Ch. Tsamatos (2002)

Annales Polonici Mathematici

We introduce the notion of uniform quietness at zero for a real-valued function and we study one-parameter nonlocal boundary value problems for second order differential equations involving such functions. By using the Krasnosel'skiĭ fixed point theorem in a cone, we give values of the parameter for which the problems have at least two positive solutions.

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