Positive solutions of nonlinear systems via the vector version of Krasnoselskii’s fixed point theorem in cones
AbstractThe vector version of Krasnoselskii’s fixed point theorem in cones is used to obtain existence and localization results for the…
not-at-ICTP
The nonlinear heat equation via fixed point principles
Abstract Starting with the existence and uniqueness result of J.L.Lions for the non-homogenous heat equation with the source term in…
Positive solutions of nonlinear singular integral equations in ordered Banach spaces
AbstractIn this paper a new version of Krasnoselskii’s fixed point theorem in cones, together with a global weak Harnack inequality…
Aronszajn type theorems for integral equations on unbounded domains via maximal solutions
Abstract This paper discusses the topological structure of the solution set of a general Volterra integral equation. Under natural conditions…
Note on the abstract generalized quasilinearization method
Abstract The abstract generalized quasilinearization method established in [2] for ordered Banach spaces with regular or normal cone and continuous…
Construction of upper and lower solutions with applications to singular boundary value problems
Abstract An upper and lower solution theory is presented for the Dirichlet boundary value problem \(y^{\prime\prime}+f(t,y,y^{\prime})=0\), \(0<t <1\) with \(y(0)=y(1)=0\).…
Existence and localization results for semi-linear problems
AbstractThis survey paper presents the new method worked out in [14] and [15] for the existence and localization of solutions…
Compression-expansion fixed point theorems in two norms
AbstractIn this paper we present compression-expansion fixed point theorems in cones where the compression and the expansion conditions are expressed…
Boundary value problems arising in the percolation of water from a cylindrical reservoir into the surrounding soil
Abstract Existence results are established for a general class of second-order boundary value problems motivated from a problem arising in…
Compression-expansion fixed point theorem in two norms and applications
Abstract In this paper we present a two-norms version of Krasnoselskii’s fixed point theorem in cones. The abstract result is…