Fractional Differential Equations

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Nonlinear Functional Analysis And Its Applications

computational fluid mechanics and heat transfer is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the computational fluid mechanics and heat transfer is universally compatible with any devices to read.

Computational Fluid Mechanics And Heat Transfer

Linear Differential Operators By Prof. Cornelius Lanczos. Pp. xvi + 564. (London: D. Van Nostrand Co., Ltd.; New York: D. Van Nostrand Company, Inc., 1961.) 80s.

Linear Differential Operators

Positive solutions of nonlinear fractional differential equations with integral boundary value conditions

The authors give sufficient conditions for the existence of at least three classical solutions to the nonlinear impulsive fractional boundary value problem with a p-Laplacian and Dirichlet conditions $$\begin{aligned} {\left\{ \begin{array}{ll} D^{\alpha }_{T^-}\varPhi _p(^cD^{\alpha }_{0^+}u(t))+|u(t)|^{p-2}u(t)= \lambda f(t,u(t)), &{}t\ne t_j,\ \ t\in (0,T),\\ \varDelta (D^{\alpha -1}_{T^-}\varPhi _p(^cD^{\alpha }_{0^+}u))(t_j)=I_j(u(t_j)),\\ u(0)=u(T)=0, \end{array}\right. } \end{aligned}$$
 where $$\alpha \in (\frac{1}{p}, 1]$$
 and $$p > 1$$
 . Their approach is based on variational methods. The main result is illustrated with an example.

Three Solutions for Impulsive Fractional Boundary Value Problems with $${\mathbf {p}}$$ p -Laplacian

/pdf/a-telescoping-principle-for-oscillation-of-second-order-2keium1768.pdf

A Telescoping Principle for Oscillation of Second Order Differential Equations on a Time Scale

We consider the following boundary value problem with nonhomogeneous three-point boundary condition 

$$ \begin{array}{l} \left( {\phi _p ( {u^\prime } )} \right)^{\prime\prime} + a( t )f( u ) = 0, \quad t \in ( {0,1} ), \\ u( 0 ) = \xi u( \eta ) + \lambda , \quad u^\prime ( 0 ) = u^\prime( 1 ) = 0 \\ \end{array}$$

 We derive several existence, nonexistence, and multiplicity results for positive solutions in terms of different values of the parameter λ The uniqueness of positive solutions and the dependence of positive solutions on the parameter λ are also studied

Positive Solutions for Third Order Boundary Value Problems with p-Laplacian

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation
\begin{equation*}
-\Delta \big(a(k)\phi_p(\Delta u(k-1))\big)+b(k)\phi_p(u(k))=\lambda f(k,u(k))),\quad k\in\mathbb{Z},
\end{equation*}
where $p>1$ is a real number, $\phi_p(t)=|t|^{p-2}t$ for $t\in\mathbb{R}$,
$\lambda>0$ is a parameter, $a, b:\mathbb{Z}\to (0,\infty)$, and
$f: \mathbb{Z}\times\mathbb{R}\to\mathbb{R}$ is continuous in the second variable.
Related results in the literature are extended.

Existence of homoclinic solutions for second order difference equations with $p$-laplacian

We consider a boundary value problem for the beam equation. 
Some a priori estimates to the positive solutions of this problem are obtained.
 Sufficient conditions for the existence, nonexistence, and uniqueness of positive solutions
for the boundary value problem are established.

Lingju Kong

Papers

Three Solutions for Impulsive Fractional Boundary Value Problems with $${\mathbf {p}}$$ p -Laplacian

A Telescoping Principle for Oscillation of Second Order Differential Equations on a Time Scale

Positive Solutions for Third Order Boundary Value Problems with p-Laplacian

Existence of homoclinic solutions for second order difference equations with $p$-laplacian

Existence, Nonexistence, and Uniqueness of Positive Solutions to a Three Point Fourth Order Boundary Value Problem