scholarly journals Existence and multiplicity of solutions for a class of quasilinear problems in Orlicz–Sobolev spaces

2016 ◽  
Vol 62 (6) ◽  
pp. 767-785 ◽  
Author(s):  
Karima Ait-Mahiout ◽  
Claudianor O. Alves
Keyword(s):  
Sobolev Spaces ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Problems

scholarly journals Multiple Solutions for Nonlinear Navier Boundary Systems Involving(p1(x),…,pn(x))-Biharmonic Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Qing Miao
Keyword(s):  
Variational Principle ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Variable Exponent ◽  
Multiplicity Of Solutions ◽  
Biharmonic Problem ◽  
Existence And Multiplicity ◽  
Variable Exponent Sobolev Spaces

We improve some results on the existence and multiplicity of solutions for the(p1(x),…,pn(x))-biharmonic system. Our main results are new. Our approach is based on general variational principle and the theory of the variable exponent Sobolev spaces.

scholarly journals Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz–Sobolev spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Heidari ◽  
A. Razani
Keyword(s):  
Variational Methods ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Elliptic Systems ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

AbstractIn this paper, we study some results on the existence and multiplicity of solutions for a class of nonlocal quasilinear elliptic systems. In fact, we prove the existence of precise intervals of positive parameters such that the problem admits multiple solutions. Our approach is based on variational methods.

scholarly journals Multiplicity of solutions for mean curvature operators with minimum and maximum in Minkowski space

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yanhong Zhang ◽  
Suyun Wang
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Unbounded Operator ◽  
Degree Theory ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Problems

AbstractIn this paper, we study the existence and multiplicity of solutions of the quasilinear problems with minimum and maximum $$\begin{aligned}& \bigl(\phi \bigl(u'(t)\bigr)\bigr)'=(Fu) (t),\quad \mbox{a.e. }t\in (0,T), \\& \min \bigl\{ u(t) \mid t\in [0,T]\bigr\} =A, \qquad \max \bigl\{ u(t) \mid t\in [0,T]\bigr\} =B, \end{aligned}$$ (ϕ(u′(t)))′=(Fu)(t),a.e. t∈(0,T),min{u(t)∣t∈[0,T]}=A,max{u(t)∣t∈[0,T]}=B, where $\phi :(-a,a)\rightarrow \mathbb{R}$ϕ:(−a,a)→R ($0< a<\infty $0<a<∞) is an odd increasing homeomorphism, $F:C^{1}[0,T]\rightarrow L^{1}[0,T]$F:C1[0,T]→L1[0,T] is an unbounded operator, $T>1$T>1 is a constant and $A, B\in \mathbb{R}$A,B∈R satisfy $B>A$B>A. By using the Leray–Schauder degree theory and the Brosuk theorem, we prove that the above problem has at least two different solutions.

scholarly journals Existence and multiplicity of solutions for a fractional p-Laplacian equation with perturbation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhen Zhi ◽  
Lijun Yan ◽  
Zuodong Yang
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Analytical Techniques ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

AbstractIn this paper, we consider the existence of nontrivial solutions for a fractional p-Laplacian equation in a bounded domain. Under different assumptions of nonlinearities, we give existence and multiplicity results respectively. Our approach is based on variational methods and some analytical techniques.

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