scholarly journals ON BOUNDED PSEUDO AND WEAK SOLUTIONS OF A NONLINEAR DIFFERENTIAL EQUATION IN BANACH SPACES

1999 ◽  
Vol 32 (2) ◽  
Author(s):  
Slawomir Krzyska ◽  
Ireneusz Kubiaczyk
Keyword(s):  
Differential Equation ◽  
Banach Spaces ◽  
Nonlinear Differential Equation ◽  
Weak Solutions

scholarly journals Uniqueness of weak solutions to a prion equation with polymer joining

Analysis ◽  
2017 ◽  
Vol 37 (2) ◽  
Author(s):  
Elena Leis ◽  
Christoph Walker
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlinear Differential Equation ◽  
Weak Solutions ◽  
Reaction Rates ◽  
Global Weak Solutions ◽  
Polymer Joining

AbstractWe consider a model for prion proliferation that includes prion polymerization, polymer splitting, and polymer joining. The model consists of an ordinary differential equation for the prion monomers and a hyperbolic nonlinear differential equation with integral terms for the prion polymers and was shown to possess global weak solutions for unbounded reaction rates [

scholarly journals Weak solutions for nonlinear fractional differential equation with fractional separated boundary conditions in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1117-1125 ◽  
Author(s):  
Hamza Rebai ◽  
Djamila Seba
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Weak Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Weak Solutions ◽  
Separated Boundary Conditions ◽  
Fractional Differential ◽  
Measures Of Weak Noncompactness

This paper deals with nonlinear fractional differential equation with fractional separated boundary conditions. We investigate the existence of weak solutions in Banach spaces. To obtain such result we apply an appropriate fixed point theorem and the technique of measures of weak noncompactness. An example illustrating the theory is given.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

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