Infinitely Many Solutions for Fractional p-Kirchhoff Equations
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DOI: 10.1007/s00009-018-1124-x
Abstract: In this paper we consider the existence of infinitely many weak solutions for fractional Schrödinger–Kirchhoff problems. Precisely speaking, we investigate $$\begin{aligned} \left\{ \begin{array}{cl} M\left( \int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\mathrm{d}x\mathrm{d}y\right) (-\triangle )_p^su+V(x)|u|^{p-2}u=f(x,u), &{}\quad \mathrm{in}~\Omega ,\\ u=0, &{}\quad \mathrm{in}~\mathbb… read more here.
Keywords: kirchhoff; solutions fractional; many solutions; infinitely many ... See more keywords
Solution of the Kirchhoff–Plateau Problem
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DOI: 10.1007/s00332-017-9359-4
Abstract: The Kirchhoff–Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a… read more here.
Keywords: plateau problem; kirchhoff; kirchhoff plateau; loop ... See more keywords
Existence of Positive Solution for Kirchhoff Problems
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DOI: 10.1007/s11785-017-0709-x
Abstract: In this work, we study the following Kirchhoff type problem $$\begin{aligned} \begin{gathered} -\Big (a+b\int _{\Omega }|\nabla u|^pdx\Big )\Delta _p u =g(x)u^{-\gamma }+\lambda f(x,u),\quad \text {in }\Omega , \\ u=0, \quad \text {on }\partial \Omega ,… read more here.
Keywords: kirchhoff; solution kirchhoff; existence positive; positive solution ... See more keywords
Least-energy nodal solutions of critical Kirchhoff problems with logarithmic nonlinearity
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DOI: 10.1007/s13324-020-00386-z
Abstract: In this paper, we are concerned with the existence of least energy sign-changing solutions for the following fractional Kirchhoff problem with logarithmic and critical nonlinearity: $$\begin{aligned} \left\{ \begin{array}{ll} \left( a+b[u]_{s,p}^p\right) (-\Delta )^s_pu = \lambda |u|^{q-2}u\ln… read more here.
Keywords: least energy; energy sign; kirchhoff; nonlinearity ... See more keywords
Existence and Asymptotic Behavior of Solutions for Degenerate Nonlinear Kirchhoff Strings with Variable-Exponent Nonlinearities
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DOI: 10.1007/s40306-021-00420-7
Abstract: In this paper, we investigate the existence of a local solution in time and discuss the exponential asymptotic behavior to a weakly damped wave equation involving the variable-exponents u t t − M ∇ u… read more here.
Keywords: left right; asymptotic behavior; kirchhoff; right vert ... See more keywords
On a Class of Critical p-Biharmonic Kirchhoff Type Problems with Indefinite Weights
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DOI: 10.1007/s41980-020-00436-z
Abstract: Using the genus theory introduced by Krasnoselskii and a variant of the mountain pass theorem due to Rabinowitz [24], we study the existence of solutions for the following Kirchhoff type problem: $$\begin{aligned} {\left\{ \begin{array}{ll} M\left(… read more here.
Keywords: class critical; kirchhoff; delta; partial partial ... See more keywords
Self-contact in closed and open Kirchhoff rods
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DOI: 10.1016/j.ijnonlinmec.2021.103786
Abstract: Abstract We consider the problem of an impenetrable Kirchhoff rod in self-contact. The contact is assumed to be frictionless and of point-contact type. The self-contacted rod is modeled as a set of contact-free segments each… read more here.
Keywords: contact; contact closed; closed open; rod ... See more keywords
A perturbed Kirchhoff problem with critical exponent
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DOI: 10.1080/00036811.2019.1687884
Abstract: ABSTRACT In this paper, we consider a class of Kirchhoff problems as follows (1) where a, b>0 are given constants, ϵ is a small parameter and . We first prove the nondegeneracy of positive solutions… read more here.
Keywords: perturbed kirchhoff; kirchhoff problem; kirchhoff; critical exponent ... See more keywords
Stability and instability for a viscoelastic Kirchhoff heat equation with variable sources
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DOI: 10.1080/00036811.2025.2450692
Abstract: This work is devoted to studying the existence and nonexistence of global weak solutions for the following class of diffusion equations of Kirchhoff type with viscoelastic term and variable exponent sources \[ u_t-M\left(\left \Vert \nabla… read more here.
Keywords: equation; vert; weak solutions; kirchhoff ... See more keywords
Infinitely many solutions for non-local elliptic non-degenerate p-Kirchhoff equations with critical exponent
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DOI: 10.1080/17476933.2019.1627527
Abstract: ABSTRACT In this paper, we obtain the existence of infinitely many weak solutions with negative energy for non-degenerate elliptic Kirchhoff equation with critical exponent driven by the fractional p-Laplacian. We show this result when is… read more here.
Keywords: non degenerate; critical exponent; kirchhoff; infinitely many ... See more keywords
Critical fractional p-Kirchhoff type problem with a generalized Choquard nonlinearity and magnetic field
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DOI: 10.1080/17476933.2024.2336971
Abstract: In this article, we establish the fractional version of concentration compactness principle to study the existence of solutions for the critical fractional p-Kirchhoff problem with magnetic field, a generalized Choquard nonlinearity, and the Kirchhoff function… read more here.
Keywords: generalized choquard; choquard nonlinearity; fractional kirchhoff; magnetic field ... See more keywords