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Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations

Luisa MalagutiValentina Taddei — 2005

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The paper deals with the quasi-linear ordinary differential equation ( r ( t ) ϕ ( u ' ) ) ' + g ( t , u ) = 0 with t [ 0 , ) . We treat the case when g is not necessarily monotone in its second argument and assume usual conditions on r ( t ) and ϕ ( u ) . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano, [Acta...

Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem

Irene BenedettiLuisa MalagutiValentina Taddei — 2011

Mathematica Bohemica

The paper deals with the multivalued boundary value problem x ' A ( t , x ) x + F ( t , x ) for a.a. t [ a , b ] , M x ( a ) + N x ( b ) = 0 , in a separable, reflexive Banach space E . The nonlinearity F is weakly upper semicontinuous in x . We prove the existence of global solutions in the Sobolev space W 1 , p ( [ a , b ] , E ) with 1 < p < endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneous linearized problem. An example completes the discussion.

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