scholarly journals On the Existence of Nontrivial Solutions for Nonlocal Elliptic Kirchhoff Type Problems with Nonlinear Boundary Conditions

2015 ◽  
Vol 55 (1) ◽  
pp. 183-188
Author(s):  
S. H. Rasouli ◽  
B. Salehi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Type Equation ◽  
Nonlinear Boundary Conditions ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Nontrivial Solutions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Kirchhoff Type Problems

Abstract In this paper, by using the Mountain Pass Lemma, we study the existence of nontrivial solutions for a nonlocal elliptic Kirchhoff type equation together with nonlinear boundary conditions.

scholarly journals Nontrivial Solutions for Time Fractional Nonlinear Schrödinger-Kirchhoff Type Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
N. Nyamoradi ◽  
Y. Zhou ◽  
E. Tayyebi ◽  
B. Ahmad ◽  
A. Alsaedi
Keyword(s):  
Variational Methods ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Type Equation ◽  
Nontrivial Solutions ◽  
Nonlinear Schrödinger ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Left And Right

We study the existence of solutions for time fractional Schrödinger-Kirchhoff type equation involving left and right Liouville-Weyl fractional derivatives via variational methods.

Concentrating Bound States for Kirchhoff Type Problems in ℝ3 Involving Critical Sobolev Exponents

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
Yi He ◽  
Gongbao Li ◽  
Shuangjie Peng
Keyword(s):  
Weak Solutions ◽  
Bound States ◽  
Type Equation ◽  
Positive Parameter ◽  
Kirchhoff Type ◽  
Critical Sobolev Exponents ◽  
Kirchhoff Type Equation ◽  
Small Positive Parameter ◽  
Kirchhoff Type Problems

AbstractWe study the concentration and multiplicity of weak solutions to the Kirchhoff type equation with critical Sobolev growth,where ε is a small positive parameter and a, b > 0 are constants, f ∈ C

Blow-up of solutions for a Kirchhoff type equation with variable-exponent nonlinearities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammad Shahrouzi ◽  
Firoozeh Kargarfard
Keyword(s):  
Variable Exponent ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Type Equation ◽  
Initial Energy ◽  
Kirchhoff Type ◽  
Positive Initial Energy ◽  
Kirchhoff Type Equation ◽  
Upper Bound Estimate

AbstractThis paper deals with a Kirchhoff type equation with variable exponent nonlinearities, subject to a nonlinear boundary condition. Under appropriate conditions and regarding arbitrary positive initial energy, it is proved that solutions blow up in a finite time. Moreover, we obtain the upper bound estimate of the blow-up time.

scholarly journals Nontrivial Solutions for Asymmetric Kirchhoff Type Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ruichang Pei ◽  
Jihui Zhang
Keyword(s):  
Nontrivial Solution ◽  
Mountain Pass Theorem ◽  
Existence Results ◽  
Mountain Pass ◽  
Nontrivial Solutions ◽  
Kirchhoff Type ◽  
Positive Semiaxis ◽  
Asymmetric Growth ◽  
Trudinger Inequality ◽  
Kirchhoff Type Problems

We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at+∞and−∞inℝN(N=2,3). Namely, it is 4-linear at−∞and 4-superlinear at+∞. However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by combining Mountain Pass Theorem and a variant version of Mountain Pass Theorem with Moser-Trudinger inequality.

Existence results for a Kirchhoff type equation in Orlicz–Sobolev spaces

2017 ◽  
Vol 8 (3) ◽  
Author(s):  
EL Miloud Hssini ◽  
Najib Tsouli ◽  
Mustapha Haddaoui
Keyword(s):  
Variational Principle ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Type Equation ◽  
Existence Results ◽  
Mountain Pass ◽  
Nonlocal Problems ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation

AbstractIn this paper, based on the mountain pass theorem and Ekeland’s variational principle, we show the existence of solutions for a class of non-homogeneous and nonlocal problems in Orlicz–Sobolev spaces.

scholarly journals Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions

2016 ◽  
Vol 34 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Mohammed Berrajaa ◽  
Omar Chakrone ◽  
Fatiha Diyer ◽  
Okacha Diyer
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Minimization Method ◽  
The First Eigenvalue

In this paper we study the existence of at least two nontrivial solutions for the nonlinear problem p-Laplacian, with nonlinear boundary conditions. We establish that there exist at least two solutions, which are opposite signs. For this reason, we characterize the first eigenvalue of an intermediary eigenvalue problem by the minimization method. In fact, in some sense, we establish the non-resonance below the first eigenvalues of nonlinear Steklov-Robin.

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