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A third order boundary value problem subject to nonlinear boundary conditions

Gennaro Infante, Paolamaria Pietramala (2010)

Mathematica Bohemica

Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.

A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces

Anastasie Gudovich, Mikhail Kamenski, Paolo Nistri (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset Z L ( ε ) of the solution set of the singularly perturbed system. This subset is the set of...

A topological version of the Ambrosetti-Prodi theorem

Bogdan Przeradzki (1996)

Annales Polonici Mathematici

The existence of at least two solutions for nonlinear equations close to semilinear equations at resonance is obtained by the degree theory methods. The same equations have no solutions if one slightly changes the right-hand side. The abstract result is applied to boundary value problems with specific nonlinearities.

A transmission problem

Irena Rachůnková (1992)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A unified approach to singular problems arising in the membrane theory

Irena Rachůnková, Gernot Pulverer, Ewa B. Weinmüller (2010)

Applications of Mathematics

We consider the singular boundary value problem ( t n u ' ( t ) ) ' + t n f ( t , u ( t ) ) = 0 , lim t → 0 + t n u ' ( t ) = 0 , a 0 u ( 1 ) + a 1 u ' ( 1 - ) = A , where f ( t , x ) is a given continuous function defined on the set ( 0 , 1 ] × ( 0 , ∞ ) which can have a time singularity at t = 0 and a space singularity at x = 0 . Moreover, n ∈ ℕ , n ≥ 2 , and a 0 , a 1 , A are real constants such that a 0 ∈ ( 0 , ∞ ) , whereas a 1 , A ∈ [ 0 , ∞ ) . The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested in...

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