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http://hdl.handle.net/10174/40
2020-02-28T07:30:43ZOn heteroclinic solutions for BVPs involving φ-Laplacian operators without asymptotic or growth assumptions
http://hdl.handle.net/10174/27224
Title: On heteroclinic solutions for BVPs involving φ-Laplacian operators without asymptotic or growth assumptions
Authors: Minhós, Feliz
Abstract: In this paper we consider the second order discontinuous equation in the real line,
(φ(a(t)u′(t)))′ = f(t,u(t),u′(t)), a.e.t∈R,
u(-∞) = A, u(+∞)=B,
with φ an increasing homeomorphism such that φ(0)=0 and φ(R)=R, a∈C(R) with a(t)>0, for t∈ℝ, f:R³→R a L¹-Carathéodory function and A,B∈ℝ verifying an adequate relation.
We remark that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities φ and f. Moreover, as far as we know, our main result is even new when φ(y)=y, that is, for equation
(a(t)u′(t))′=f(t,u(t),u′(t)), a.e.t∈R.2019-03-31T23:00:00ZLocalization results for impulsive second order coupled systems on the half-line and application to logging timber by helicopter
http://hdl.handle.net/10174/27223
Title: Localization results for impulsive second order coupled systems on the half-line and application to logging timber by helicopter
Authors: Minhós, Feliz
Abstract: This work considers a second order impulsive coupled system with full nonlinearities, generalized impulse functions and mixed boundary conditions. This is the first time where such coupled systems are considered with nonlinearities with dependence on both unknown functions and their derivatives, together impulsive functions given by more general framework allowing jumps on the both functions and both derivatives
The arguments apply the fixed point theory, Green's functions technique, L¹-Carathéodory functions theory and Schauder's fixed point theorem.
An application to the transverse vibration system of elastically coupled double-string is presented in last section.2019-01-01T00:00:00ZHeteroclinic solutions for classical and singular φ-Laplacian non-autonomous differential equations
http://hdl.handle.net/10174/27068
Title: Heteroclinic solutions for classical and singular φ-Laplacian non-autonomous differential equations
Authors: Minhós, Feliz
Abstract: In this paper, we consider the second order discontinuous differential equation in the real line, (a(t,u)ϕ(u′))′=f(t,u,u′),a.e.t∈R,u(−∞)=ν−,u(+∞)=ν+, with ϕ an increasing homeomorphism such that ϕ(0)=0 and ϕ(R)=R, a∈C(R2,R) with a(t,x)>0 for (t,x)∈R2, f:R3→R a L1-Carathéodory function and ν−,ν+∈R such that ν−<ν+. The existence and localization of heteroclinic connections is obtained assuming a Nagumo-type condition on the real line and without asymptotic conditions on the nonlinearities ϕ and f. To the best of our knowledge, this result is even new when ϕ(y)=y, that is for equation (a(t,u(t))u′(t))′=f(t,u(t),u′(t)),a.e.t∈R. Moreover, these results can be applied to classical and singular ϕ-Laplacian equations and to the mean curvature operator.2019-02-15T00:00:00ZOn multipoint resonant problems on the half-line
http://hdl.handle.net/10174/27067
Title: On multipoint resonant problems on the half-line
Authors: López-Somoza, Lucía; Minhós, Feliz
Abstract: In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multipoint second-order boundary value problem, with a fully differential equation.
The noninvertibility of the linear part is overcome by a new perturbation technique, which allows obtaining an existence result and a localization theorem. Our hypotheses are clearly much less restrictive than those existent in the literature and, moreover, they can be applied to higher-order, resonant or nonresonant, boundary value problems defined on the half-line or even on the real line.2019-02-15T00:00:00Z