Displaying similar documents to “An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing and superlinear nonlinearities.”

Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach

Haishen Lü, Donal O'Regan, Ravi P. Agarwal (2007)

Applications of Mathematics

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This paper studies the existence of solutions to the singular boundary value problem - u ' ' = g ( t , u ) + h ( t , u ) , t ∈ ( 0 , 1 ) , u ( 0 ) = 0 = u ( 1 ) , where g ( 0 , 1 ) × ( 0 , ∞ ) → ℝ and h ( 0 , 1 ) × [ 0 , ∞ ) → [ 0 , ∞ ) are continuous. So our nonlinearity may be singular at t = 0 , 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.

Fractional BVPs with strong time singularities and the limit properties of their solutions

Svatoslav Staněk (2014)

Open Mathematics

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In the first part, we investigate the singular BVP d d t c D α u + ( a / t ) c D α u = ℋ u , u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where ℋ is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems d d t c D α n u + ( a / t ) c D α n u = f ( t , u , c D β n u ) , u(0) = A, u(1) = B, c D α n u ( t ) t = 0 = 0 where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t,...

Positive and maximal positive solutions of singular mixed boundary value problem

Ravi Agarwal, Donal O’Regan, Svatoslav Staněk (2009)

Open Mathematics

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The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.