in which the second derivative may occur nonlinearly. Positive solutions for the case f (t,u,uâ€²,uâ€²â€²) = g(t)h(u) have been studied by Ma [15] and Webb [20, 21], when f (t,u,uâ€²,uâ€²â€²) = h(t,u) by He andâ€¦ (More)

*Correspondence: ruben.figueroa@usc.es 1Departamento de AnÃ¡lise MatemÃ¡tica, Facultade de MatemÃ¡ticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain Full list of authorâ€¦ (More)

We prove new results on the existence of positive solutions for some cantilever equation subject to nonlocal and nonlinear boundary conditions. Our main ingredient is the classical fixed point index.

In 1998 Manickam and Singhi conjectured that for every positive integer d and every n â‰¥ 4d, every set of n real numbers whose sum is nonnegative contains at least ( nâˆ’1 dâˆ’1 ) subsets of size d whoseâ€¦ (More)

Using Ekelandâ€™s variational principle we give a critical point theorem of Schechter type for extrema on a sublevel set in a Banach space. This result can be applied to localize the solutions of PDEsâ€¦ (More)

In this note we investigate the topological structure of the mild solution set of nonlocal Cauchy problems governed by semilinear differential inclusions in separable Banach spaces. We show that theâ€¦ (More)

Our aim in this paper is to find decay mild solutions of the nonlocal Cauchy problem for a class of second order evolution equations with memory. By constructing a suitable measure of noncompactnessâ€¦ (More)