Existence of Multiple Solutions of a Kirchhoff Type $p$-Laplacian Equation on the Sierpiński Gasket
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DOI: 10.1007/s10440-019-00283-z
Abstract: In this paper, we study the following boundary value problem involving the weak $p$-Laplacian. $$ -M\bigl(\|u\|_{\mathcal{E}_{p}}^{p}\bigr)\Delta _{p} u = h(x,u) \quad \text{in}\ \mathcal{S}\setminus \mathcal{S}_{0}; \quad u = 0 \ \text{on}\ \mathcal{S}_{0}, $$ where $\mathcal{S}$ is… read more here.
Keywords: multiple solutions; kirchhoff type; existence multiple; solutions kirchhoff ... See more keywords
Existence of Multiple Solutions for a Class Non-uniformly Elliptic Equations with Critical Exponential Growth
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DOI: 10.1007/s41980-018-0033-x
Abstract: This paper deals with the existence and multiplicity of weak solutions to non-uniformly elliptic problem $$\begin{aligned} -\text {div}(a(x,\nabla u))+V(x)\vert u\vert ^{N-2} u=\lambda \Bigg (\exp \Bigg (\alpha \vert u\vert ^{\frac{N}{N-1}}\Bigg )+f(x,u)\Bigg ), \end{aligned}$$-div(a(x,∇u))+V(x)|u|N-2u=λ(exp(α|u|NN-1)+f(x,u)),in $$\mathbb {R}^N$$RN, where… read more here.
Keywords: solutions class; vert; uniformly elliptic; multiple solutions ... See more keywords
On a class of stationary loops on SO(n)$\mathbf{SO}(n)$ and the existence of multiple twisting solutions to a nonlinear elliptic system subject to a hard incompressibility constraint
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DOI: 10.1186/s13661-018-1047-2
Abstract: AbstractIn this paper we consider the second order nonlinear elliptic system in divergence and variational form {div[Fξ(|x|,|∇u|2)∇u]=[cof∇u]∇Pin U,det∇u=1in U,u=φon ∂U, $$\begin{aligned} \textstyle\begin{cases} \operatorname{div}[ F_{\xi }(\vert x\vert ,\vert \nabla u\vert ^{2})\nabla u ] = [ \operatorname{cof}\nabla u] \nabla \mathscr{P}… read more here.
Keywords: system; nonlinear elliptic; twisting solutions; elliptic system ... See more keywords
Existence of multiple positive solutions for fractional Laplace problems with critical growth and sign-changing weight in non-contractible domains
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DOI: 10.1186/s13661-019-1193-1
Abstract: We prove the existence of multiple positive solutions for a fractional Laplace problem with critical growth and sign-changing weight in non-contractible domains. read more here.
Keywords: solutions fractional; fractional laplace; positive solutions; critical growth ... See more keywords
Existence and multiple solutions to a discrete fourth order boundary value problem
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DOI: 10.1186/s13662-018-1879-1
Abstract: In this article, we study a discrete fourth order boundary value problem. By making use of variational methods and critical point theory, we obtain some criteria for the existence and multiple solutions. Moreover, two examples… read more here.
Keywords: existence multiple; fourth order; value problem; boundary value ... See more keywords
Codiagonalization of Matrices and Existence of Multiple Homoclinic Solutions
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DOI: 10.11948/2017012
Abstract: The purpose of this paper is twofold. First, we use Lagrange’s method and the generalized eigenvalue problem to study systems of two quadratic equations. We find exact conditions so the system can be codiagonalized and… read more here.
Keywords: codiagonalization; codiagonalization matrices; homoclinic solutions; multiple homoclinic ... See more keywords
Co-existence of multiple trade-off currencies shapes evolutionary outcomes
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DOI: 10.1371/journal.pone.0189124
Abstract: Evolutionary studies often assume that energy is the primary resource (i.e. “currency”) at the heart of the survival-reproduction trade-off, despite recent evidence to the contrary. The evolutionary consequences of having a single trade-off currency versus… read more here.
Keywords: trade currencies; multiple currencies; currencies shapes; trade ... See more keywords