• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.359-380
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• 2017

This paper is concerned with a kind of boundary value problem for singular second order differential systems with Laplacian operators. Using a multiple fixed point theorem, sufficient conditions to guarantee the existence of at least three positive solutions of this kind of boundary value problem are established. An example is presented to illustrate the main results.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.295-306
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• 2006

In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of 2m or 2m + 1 symmetric positive solutions of fourth-order two point boundary value problem y(4)(t) - f(t, y(t), y"(t))= 0, y(0) = y(1) = y'(0) = y"(1)=0.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.257-271
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• 2013

In this article, we establish the existence of at least three unbounded positive solutions to a boundary-value problem of the nonlinear singular fractional differential equation. Our analysis relies on the well known fixed point theorems in the cones.

• East Asian mathematical journal
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• v.40 no.3
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• pp.295-306
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• 2024

We investigate the existence of multiple positive solutions of the following elliptic equation with a Schrödinger-type term: $$\begin{cases}-{\Delta}u+V(x)u={\lambda}f(u){\quad} x{\in}{\Omega},\\{\qquad}{\qquad}{\quad}u=0, {\qquad}\;x{\in}\partial{\Omega},\end{cases}$$, where 0 ∈ Ω is a bounded domain in ℝ^N , N ≥ 1, with a smooth boundary ∂Ω, f ∈ C[0, ∞), V ∈ L^∞(Ω) and λ is a positive parameter. In particular, when f(s) > 0 for 0 ≤ s < σ and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.239-245
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• 2012

We prove that an asymmetric beam equation has at least two solutions, one of which is a positive solution. To prove the existence of the other solution, we use linking inequalities.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.943-956
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• 2000

We investigate a relation between multiplicity of solutions and source terms of jumping problem in wave equation when the nonlinearity crosses an eigenvalue and the source term is generated by finite eigenfunctions. We also show that the jumping problem has infinitely many solutions when the source term is positive multiple of the positve eigenfunction.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.79-87
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• 2009

This paper deals with the multipoint boundary value problem for one dimensional p-Laplacian $({\phi}_p(u'))'(t)$ + f(t,u(t)) = 0, $t{\in}$ (0, 1), subject to the boundary value conditions: u'(0) - $\sum\limits^n_{i=1}{\alpha_i}u({\xi}_i)$ = 0, u'(1) + $\sum\limits^n_{i=1}{\alpha_i}u({\eta}_i)$ = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1109-1118
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• 2009

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

• East Asian mathematical journal
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• v.34 no.5
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• pp.703-713
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• 2018

Let $N{\geq}3$, $2^*=2N/(N-2)$ and $p{\in}(2,2^*)$. Our purpose in this paper is to consider multiple existence of solutions of problem $$-{\Delta}u-{\frac{\mu}{{\mid}x{\mid}^2}}+{\alpha}u={\mid}u{\mid}^{p-2}u+{\lambda}f\;u{\in}H^1({\mathbb{R}}^n)$$, where a, ${\lambda}$ > 0, ${\mu}{\in}(0,(N-2)^2/4)f{\in}H^{-1}({\mathbb{R}}^N)$, $f{\geq}0$ and $f{\neq}0$.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.221-236
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• 1997

In this paper we investigate the multiplicity of positive solutions to a quasilinear Neumann problem; $$ {\varepsilon^m div($\mid$\bigtriangledown_u$\mid$^{m-2}\bigtriangledown_u) - u$\mid$u$\mid$^{m-2} + u$\mid$u$\mid$^{m-2} + u$\mid$u$\mid$^{p-2} = 0 in \omega $$ $$ \frac{\partial u}{\partial \nu} = 0 on \partial \omega, $$ making use of Ljusternik Schnirelmann category theory.