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

Similarity:

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

Similarity:

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

Similarity:

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.

Dead cores of singular Dirichlet boundary value problems with φ -Laplacian

Ravi P. Agarwal, Donal O&amp;#039;Regan, Staněk, Svatoslav (2008)

Applications of Mathematics

Similarity:

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem ( φ ( u ' ) ) ' = λ f ( t , u , u ' ) , u ( 0 ) = u ( T ) = A . Here λ is the positive parameter, A > 0 , f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable.