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1

Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian

Shilpa, Dwivedi Gaurav

Journal of Applied Analysis

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2022

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Vol. 28, nr 2

211--218

EN

In this article, we prove the existence of a solution to a nonlocal biharmonic equation with nonlinearity depending on the gradient and the Laplacian.We employ an iterative technique based on the mountain pass theorem to prove our result.

2

On a weighted elliptic equation of N-Kirchhoff type with double exponential growth

Abid Imed, Baraket Sami, Jaidane Rached

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

634--657

EN

In this work, we study the weighted Kirchhoff problem (…) where B is the unit ball of RN , σ(x)=(log(e∣x∣))N−1 , the singular logarithm weight in the Trudinger-Moser embedding, and g is a continuous positive function on R+ . The nonlinearity is critical or subcritical growth in view of Trudinger-Moser inequalities. We first obtain the existence of a solution in the subcritical exponential growth case with positive energy by using minimax techniques combined with the Trudinger-Moser inequality. In the critical case, the associated energy does not satisfy the condition of compactness. We provide a new condition for growth, and we stress its importance to check the compactness level.

3

Localized optical vortex solitons in pair plasmas

Medina Luciano

Journal of Applied Analysis

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2021

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Vol. 27, nr 1

1--12

EN

The dynamics of short intense electromagnetic pulses propagating in a relativistic pair plasma is governed by a nonlinear Schrödinger equation with a new type of focusing-defocusing saturable nonlinearity. In this context, we provide an existence theory for ring-profiled optical vortex solitons. We prove the existence of both saddle point and minimum type solutions. Via a constrained minimization approach, we prove the existence of solutions where the photon number may be prescribed, and we get the nonexistence of small-photon-number solutions.We also use the constrained minimization to compute the soliton’s profile as a function of the photon number and other relevant parameters.

4

On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian

Smejda J., Wieteska R.

Opuscula Mathematica

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2014

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Vol. 34, no. 4

851--870

EN

In this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.

5

Existence of a solution for the fractional forced pendulum

Torres C.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 1

125--142

EN

In this work we study the fractional forced pendulum equation with combined fractional derivatives - tDαT 0Dαt u( t ) + g ( u ( t )) = f ( t ), t ∈ ( 0, T ) ( 0. 1 ) u ( 0 ) = u ( T ) = 0 where ½ < α < 1, g ∈ C ( R, R ), bounded f ∈ C [ 0, T ]. Using minimization techniques form variational calculus we show that ( 0. 1 ) has a nontrivial solution.

6

Existence Result for Diﬀerential Inclusion with p(x) - Laplacian

Barnaś S.

Schedae Informaticae

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2012

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Vol. 21

41--54

EN

In this paper we study the nonlinear elliptic problem with p(x)- Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [4].

7

Existence result for hemivariational inequality involving p(x)-Laplacian

Barnaś S.

Opuscula Mathematica

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2012

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Vol. 32, no. 3

439-454

EN

In this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [J. Math. Anal. Appl. 80 (1981), 102-129].

8

On noncoercive elliptic problems with discontinuities

Halidias N.

Journal of Applied Analysis

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2003

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Vol. 9, nr 2

211-223

EN

In this paper using the critical point theory of Chang [4] for locally Lipschitz functionals we prove an existence theorem for non-coercive Neumann problems with discontinuous nonlinearities. We use the mountain-pass theorem to obtain a nontrivial solution.

9

Critical points for vector-valued functions

Lucchetti R., Revalski J., Thera M.

Control and Cybernetics

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2002

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Vol. 31, no 3

545-555

EN

This paper contains a mountain pass theorem for continuous mappings, defined on a complete metric space and taking values in a real Banach space, ordered by a closed convex cone. We use the concept of critical point introduced by Degiovanni, Lucchetti and Ribarska, and we furnish a variant of their result, allowing for a localization both of the critical point and of the critical value.